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  • 1.
    Andren, Lina J.
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Casselgren, Carl Johan
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoiding Arrays of Odd Order by Latin Squares2013Inngår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 22, nr 2, s. 184-212Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m <= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -> infinity.

  • 2.
    Andrén, Lina J.
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Casselgren, Carl Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoiding arrays of odd order by Latin squaresManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We prove that there exists a constant c such that for each pos- itive integer k every (2k+1)×(2k+1) array A on the symbols 1,...,2k+1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k+1) times in every row and column is avoidable; that is, there is a (2k+1)×(2k+1) Latin square S on the symbols 1,...,2k+1 such that for each cell (i, j) in S the symbol in (i, j) does not appear in the corresponding cell in A. This settles the last open case of a conjecture by Häggkvist.

  • 3.
    Björklund, Johanna
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Simulation relations for pattern matching in directed graphs2013Inngår i: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 485, s. 1-15Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the problem of finding the occurrences of a pattern tree t in a directed graph g, and propose two algorithms, one for preprocessing and one for searching for t in g. It is assumed that the object graph itself is large and static, and that the pattern tree is small and frequently updated. To model varying abstraction levels in the data, we work with partially ordered alphabets and compute simulation relations rather than equivalence relations. In particular, vertices and edges are labelled with elements from a pair of preorders instead of unstructured alphabets. Under the above assumptions, we obtain a search algorithm that runs in time O(height (t) . vertical bar t vertical bar . vertical bar(V-g(+/-)t/R-g(+/-)t vertical bar(2)) where vertical bar (V-g(+/-)t/R-g(+/-)t)vertical bar is the number of equivalence classes in the coarsest simulation relation R-g(+/-)t on the graph g((+/-))t, the disjoint union of g and t. This means that the size of the object graph only affects the running time of the search algorithm indirectly, because of the groundwork done by the preprocessing routine in time O(k . vertical bar g vertical bar . vertical bar(V-g/R-g)vertical bar(2)), where vertical bar(V-g/R-g) is the number of equivalence classes in the coarsest simulation relation R-g on g, taking k = vertical bar V-g vertical bar(2) in the general case and k = height (g) if g is acyclic.

  • 4. Cavenagh, Nicholas J.
    et al.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Partial latin squares are avoidable2006Rapport (Annet vitenskapelig)
  • 5. Cutler, Jonathan
    et al.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Latin squares with forbidden entries2004Rapport (Annet vitenskapelig)
  • 6. Cutler, Jonathan
    et al.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Latin squares with forbidden entries2006Inngår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 13, nr 1, s. R47-Artikkel i tidsskrift (Fagfellevurdert)
  • 7.
    Denley, Tristan
    et al.
    Austin Peay State University.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Extending partial latin cubes2014Inngår i: Ars combinatoria, ISSN 0381-7032, Vol. 113, s. 405-414Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In the spirit of Ryser's theorem, we prove sufficient conditions on k, and m so that k xexm Latin boxes, i.e. partial Latin cubes whose filled cells form a k x x m rectangular box, can be extended to akxnxm latin box, and also to akxnxn latin box, where n is the number of symbols used, and likewise the order of the Latin cube. We also prove a partial Evans type result for Latin cubes, namely that any partial Latin cube of order n with at most n 1 filled cells is completable, given certain conditions on the spatial distribution of the filled cells.

  • 8.
    Johansson, Robert
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Introduktion till högre studier i matematik2012 (oppl. 1)Bok (Annet vitenskapelig)
  • 9.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Shcherbak, Denys
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Enumeration of t-tuples of Mutually Orthogonal Latin Rectangles and Finite GeometriesManuskript (preprint) (Annet vitenskapelig)
  • 10.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Shcherbak, Denys
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Small youden rectangles, near youden rectangles, and their connections to other row-column designs2023Inngår i: Discrete Mathematics & Theoretical Computer Science, ISSN 1462-7264, E-ISSN 1365-8050, Vol. 25, nr 1, artikkel-id 9Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we first study k × n Youden rectangles of small orders. We have enumerated all Youden rectangles for a range of small parameter values, excluding the almost square cases where k = n − 1, in a large scale computer search. In particular, we verify the previous counts for (n, k) = (7, 3), (7, 4), and extend this to the cases (11, 5), (11, 6), (13, 4) and (21, 5). For small parameter values where no Youden rectangles exist, we also enumerate rectangles where the number of symbols common to two columns is always one of two possible values, differing by 1, which we call near Youden rectangles. For all the designs we generate, we calculate the order of the autotopism group and investigate to which degree a certain transformation can yield other row-column designs, namely double arrays, triple arrays and sesqui arrays. Finally, we also investigate certain Latin rectangles with three possible pairwise intersection sizes for the columns and demonstrate that these can give rise to triple and sesqui arrays which cannot be obtained from Youden rectangles, using the transformation mentioned above.

    Fulltekst (pdf)
    fulltext
  • 11.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Shcherbak, Denys
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Triples of Orthogonal Latin and Youden Rectangles of small order2019Inngår i: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 27, nr 4, s. 229-250Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We have performed a complete enumeration of non-isotopic triples of mutually orthogonal k × n Latin rectangles for k ≤ n ≤ 7. Here we will present a census of such triples, classified by various properties, including the order of the autotopism group of the triple. As part of this we have also achieved the first enumeration of pairwise orthogonal triples of Youden rectangles. We have also studied orthogonal triples of k×8 rectangles which are formed by extending mutually orthogonal triples with non-trivial autotopisms one row at a time, and requiring that the autotopism group is non-trivial in each step. This class includes a triple coming from the projective plane of order 8. Here we find a remarkably symmetrical pair of triples of 4 × 8 rectangles, formed by juxtaposing two   selected copies of complete sets of MOLS of order 4.

  • 12.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Shcherbak, Denys
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Enumeration of Youden Rectangles of Small ParametersManuskript (preprint) (Annet vitenskapelig)
  • 13.
    Jäger, Gerold
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Shcherbak, Denys
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Enumeration of sets of mutually orthogonal latin rectangles2024Inngår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 31, nr 1, artikkel-id #P1.53Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study sets of mutually orthogonal Latin rectangles (MOLR), and a natural variation of the concept of self-orthogonal Latin squares which is applicable on larger sets of mutually orthogonal Latin squares and MOLR, namely that each Latin rectangle in a set of MOLR is isotopic to each other rectangle in the set. We call such a set of MOLR co-isotopic. In the course of doing this, we perform a complete enumeration of sets of t mutually orthogonal k × n Latin rectangles for k ≤ n ≤ 7, for all t < n up to isotopism, and up to paratopism. Additionally, for larger n we enumerate co-isotopic sets of MOLR, as well as sets of MOLR where the autotopism group acts transitively on the rectangles, and we call such sets of MOLR transitive. We build the sets of MOLR row by row, and in this process we also keep track of which of the MOLR are co-isotopic and/or transitive in each step of the construction process. We use the prefix stepwise to refer to sets of MOLR with this property at each step of their construction. Sets of MOLR are connected to other discrete objects, notably finite geometries and certain regular hypergraphs. Here we observe that all projective planes of order at most 9 except the Hughes plane can be constructed from a stepwise transitive MOLR.

    Fulltekst (pdf)
    fulltext
  • 14.
    Lundqvist, Signe
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Stokes, Klara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Applying the pebble game algorithm to rod configurations2023Inngår i: EuroCG 2023: Book of abstracts, 2023, artikkel-id 41Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present results on rigidity of structures of rigid rods connected in joints: rod configurations. The underlying combinatorial structure of a rod configuration is an incidence structure. Our aim is to find simple ways of determining which rod configurations admit non-trivial motions, using the underlying incidence structure.

    Rigidity of graphs in the plane is well understood. Indeed, there is a polynomial time algorithm for deciding whether most realisations of a graph are rigid. One of the results presented here equates rigidity of sufficiently generic rod configurations to rigidity of a related graph. As a consequence, itis possible to determine the rigidity of rod configurations using the previously mentioned polynomial time algorithm. We use this to show that all v3-configurations on up to 15 points and all triangle-free v3-configurations on up to 20 points are rigid in regular position, if such a realisation exists. We also conjecture that the smallest v3-configuration that is flexible in regular position is a previously known 283-configuration. 

  • 15.
    Lundqvist, Signe
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Stokes, Klara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Exploring the rigidity of planar configurations of points and rods2023Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 336, s. 68-82Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article we explore the rigidity of realizations of incidence geometries consisting of points and rigid rods: rod configurations. We survey previous results on the rigidity of structures that are related to rod configurations, discuss how to find realizations of incidence geometries as rod configurations, and how this relates to the 2-plane matroid. We also derive further sufficient conditions for the minimal rigidity of k-uniform rod configurations and give an example of an infinite family of minimally rigid 3-uniform rod configurations failing the same conditions. Finally, we construct v3-configurations that are flexible in the plane, and show that there are flexible v3-configurations for all sufficiently large values of v.

    Fulltekst (pdf)
    fulltext
  • 16.
    Lundqvist, Signe
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Stokes, Klara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    When is a planar rod configuration infinitesimally rigid?2023Inngår i: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the rigidity properties of rod configurations. Rod configurations are realizations of rank two incidence geometries as points (joints) and straight lines (rods) in the Euclidean plane, such that the lines move as rigid bodies, connected at the points. Note that not all incidence geometries have such realizations. We show that under the assumptions that the rod configuration exists and is sufficiently generic, its infinitesimal rigidity is equivalent to the infinitesimal rigidity of generic frameworks of the graph defined by replacing each rod by a cone over its point set. To put this into context, the molecular conjecture states that the infinitesimal rigidity of rod configurations realizing 2-regular hypergraphs is determined by the rigidity of generic body and hinge frameworks realizing the same hypergraph. This conjecture was proven by Jackson and Jordán in the plane, and by Katoh and Tanigawa in arbitrary dimension. Whiteley proved a version of the molecular conjecture for hypergraphs of arbitrary degree that have realizations as independent body and joint frameworks. Our result extends his result to hypergraphs that do not necessarily have realizations as independent body and joint frameworks, under the assumptions listed above.

    Fulltekst (pdf)
    fulltext
  • 17.
    Markström, Klas
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Unavoidable arrays2010Inngår i: Contributions to Discrete Mathematics, ISSN 1715-0868, Vol. 5, nr 1, s. 90-106Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An n x n array is avoidable if for each set of n symbols there is a Latin square on these symbols which diers from the array in every cell. We characterise all unavoidable square arrays with at most 2 symbols, and all unavoidable arrays of order at most 4. We also identify a number of general families of unavoidable arrays, which we conjecture to be a complete account of unavoidable arrays. Next, we investigate arrays with multiple entries in each cell, and identify a number of families of unavoidable multiple entry arrays. We also discuss fractional Latin squares, and their connections to unavoidable arrays.

    We note that when rephrasing our results as edge list-colourings of complete bipartite graphs, we have a situation where the lists of available colours are shorter than the length guaranteed by Galvin's Theorem to allow proper colourings.

  • 18.
    Nilson, Tomas
    et al.
    Mittuniversitetet.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Triple arrays and Youden squares2015Inngår i: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 75, nr 3, s. 429-451Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper addresses the question of when triple arrays can be constructed from Youden squares by removing a column together with the symbols therein, and then exchanging the role of columns and symbols. The scope of the investigation is limited to the standard case of triple arrays with $v=r+c-1$. For triple arrays with $\lambda_{cc}=1$ it is proven that they can never be     constructed in this way, and for triple arrays with $\lambda_{cc}=2$ it is proven that there always exists a suitable Youden square and a suitable column for this construction. Further, it is proven that Youden square constructed from a certain family of difference sets never give rise to triple arrays in this way but always gives rise to double arrays. Finally, it is proven that all triple arrays in the single known infinite family, the Paley triple arrays, can all be constructed in this way for some suitable choice of Youden square and column.

  • 19.
    Raman Sundström, Manya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Beauty as fit: A metaphor in mathematics?2013Inngår i: Research in Mathematics Education, Vol. 15, nr 2, s. 199-200Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Beauty, which plays a central role in the practice of mathematics, is almost absent in discussions of school mathematics. This is problematic, because students will decide whether or not to continue their studies inmathematics without having an accurate picture of what the subject is about. In order to have a discussion about how to introduce beauty into the school mathematicscurriculum, we need to have a clear idea about what beauty means. That is the aim ofthis study, with a focus on characterising beauty in mathematical proof.

  • 20.
    Raman Sundström, Manya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Mathematical fit: A first approximation2015Inngår i: Proceedings of the ninth conference of the Euorpean Society for research in Mathermatics education (CERME9) / [ed] Krainer, K Vondrova, N, Prague: Charles University , 2015, s. 185-191Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We discuss here the notion of mathematical fit, a concept that might relate to mathematical explanation and mathematical beauty. We specify two kinds of fit a proof can have, intrinsic and extrinsic, and provide characteristics that help distinguish different proofs of the same theorem.

  • 21.
    Raman Sundström, Manya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Two beautiful proofs of Pick's theorem2011Inngår i: Proceedings of Seventh Congress of European Research in Mathematics Education / [ed] Pytlak, M.; Rowland, T.;. Swoboda, E., University of Rzeszow Publishing House , 2011, s. 224-232Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present two different proofs of Pick’s theorem and analyse in what ways might be perceived as beautiful by working mathematicians. In particular, we discuss two concepts, generality and specificity, that appear to contribute to beauty in different ways. We also discuss possible implications on insight into the nature of beauty in mathematics, and how the teaching of mathematics could be impacted, especially in countries in which discussions of beauty and aesthetics are notably absent from curricular documents.

    Fulltekst (pdf)
    FULLTEXT02
  • 22.
    Raman-Sundström, Manya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Mathematical fit: a case study2018Inngår i: Philosophia mathematica, ISSN 0031-8019, E-ISSN 1744-6406, Vol. 26, nr 2, s. 184-210Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Mathematicians routinely pass judgments on mathematical proofs. A proof might be elegant, cumbersome, beautiful, or awkward. Perhaps the highest praise is that a proof is right, that is that the proof fits the theoremin an optimal way. It is also common to judge that a proof fits better than another, or that a proof does not fit a theorem at all. This paper attempts to clarify the notion of mathematical fit. We suggest six criteria that distinguish proofs as being more or less fitting, and provide examples from several different mathematical fields.

    Fulltekst (pdf)
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  • 23.
    Raman-Sundström, Manya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sinclair, Nathalie
    Faculty of Education, Simon Fraser University, CANADA.
    The Nature and Experience of Mathematical Beauty2016Inngår i: Journal of Humanistic Mathematics, E-ISSN 2159-8118, Vol. 6, nr 1, s. 3-7Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 24.
    Shcherbak, Denys
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Jäger, Gerold
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The Zero Forcing Number of Bijection Graphs2015Inngår i: Proceedings of 26th International Workshop om Combinatorial Algorithms (IWOCA 2015), Berlin-Heidelberg: Springer, 2015, Vol. 9538, s. 334-345Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The zero forcing number of a graph is a graph parameter based on a color change process, which starts with a state, where all vertices are colored either black or white. In the next step a white vertex turns black, if it is the only white neighbor of some black vertex, and this step is then iterated. The zero forcing number Z(G) is defined as the minimum cardinality of a set S of black vertices such that the whole vertex set turns black.

    In this paper we study Z(G) for the class of bijection graphs, where a bijection graph is a graph on 2n vertices that can be partitioned into two parts with n vertices each, joined by a perfect matching. For this class of graphs we show an upper bound for the zero forcing number and classify the graphs that attain this bound. We improve the general lower bound for the zero forcing number, which is Z(G)&#x2265;&#x03B4;(G)" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Z(G)≥δ(G)Z(G)≥δ(G), for certain bijection graphs and use this improved bound to find the exact value of the zero forcing number for these graphs. This extends and strengthens results of Yi (2012) about the more restricted class of so called permutation graphs.

  • 25.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A Beautiful Proof by Induction2016Inngår i: Journal of Humanistic Mathematics, E-ISSN 2159-8118, Vol. 6, nr 1, s. 73-85Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen’s proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

    A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

    Fulltekst (pdf)
    fulltext
  • 26.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A Note on Completing Partial Latin Squares2009Inngår i: The Australasian Journal of Combinatorics, ISSN 1034-4942, Vol. 45, s. 117-124Artikkel i tidsskrift (Fagfellevurdert)
  • 27.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Are Induction and Well-Ordering Equivalent?2019Inngår i: The Mathematical intelligencer, ISSN 0343-6993, E-ISSN 1866-7414, Vol. 41, nr 3, s. 33-40Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 28.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Latin Squares with Prescriptions and Restrictions2011Inngår i: The Australasian Journal of Combinatorics, ISSN 1034-4942, Vol. 51, s. 77-87Artikkel i tidsskrift (Fagfellevurdert)
  • 29.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On the intricacy of avoiding multiple-entry arrays2012Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 312, nr 20, s. 3030-3036Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let A be any n x n array on the symbols vertical bar n vertical bar = {1, . . . , n}, with at most in symbols in each cell. An n x n Latin square L on the symbols till is said to avoid A if no entry in L is present in the corresponding cell of A, and A is said to be avoidable if such a Latin square L exists. The intricacy of this problem is defined to be the minimum number of arrays into which A must be split in order to ensure that each part is avoidable. We present lower and upper bounds for the intricacy, and conjecture that the lower bound is in fact the correct answer. (C) 2012 Elsevier B.V. All rights reserved.

  • 30.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Partial latin squares are avoidable2011Inngår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 15, nr 3, s. 485-497Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A square array is avoidable if for each set of n symbols there is an n x n Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for m >= 2 any partial Latin square of order 4m - 1 is avoidable, thus concluding the proof that any partial Latin square of order at least 4 is avoidable.

  • 31.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Romarna var inte så avancerade2019Annet (Annet (populærvitenskap, debatt, mm))
  • 32.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Studentaktiv examination: ett pedagogiskt experiment2006Inngår i: Tänk efter, tänk nytt, tänk om: universitetspedagogisk konferens i Umeå 2-3 mars 2005 : konferensrapport / [ed] Margareta Erhardsson; Katarina Winka, Umeå: Universitetspedagogiskt centrum, Umeå universitet , 2006, s. 234-242Konferansepaper (Annet vitenskapelig)
  • 33.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The intricacy of avoiding arrays2005Rapport (Annet vitenskapelig)
  • 34.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The intricacy of avoiding arrays2005Manuskript (preprint) (Annet vitenskapelig)
  • 35.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The intricacy of avoiding arrays is 22006Inngår i: Discrete Mathematics, ISSN 0012-365X, Vol. 306, s. 531-532Artikkel i tidsskrift (Fagfellevurdert)
1 - 35 of 35
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