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Öhman, Lars-Daniel
Publications (10 of 27) Show all publications
Jäger, G., Markström, K., Öhman, L.-D. & Shcherbak, D. (2019). Triples of Orthogonal Latin and Youden Rectangles of small order. Journal of combinatorial designs (Print), 27(4), 229-250
Open this publication in new window or tab >>Triples of Orthogonal Latin and Youden Rectangles of small order
2019 (English)In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 27, no 4, p. 229-250Article in journal (Refereed) Published
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.

National Category
Discrete Mathematics
Identifiers
urn:nbn:se:umu:diva-158857 (URN)10.1002/jcd.21642 (DOI)000459040800001 ()2-s2.0-85059030594 (PubMedID)
Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-23Bibliographically approved
Raman-Sundström, M. & Öhman, L.-D. (2018). Mathematical fit: a case study. Philosophia mathematica, 26(2), 184-210
Open this publication in new window or tab >>Mathematical fit: a case study
2018 (English)In: Philosophia mathematica, ISSN 0031-8019, E-ISSN 1744-6406, Vol. 26, no 2, p. 184-210Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Cary: Oxford University Press, 2018
Keywords
Fit, aesthetics, explanation
National Category
Philosophy Mathematics
Research subject
Aesthetics; Mathematics
Identifiers
urn:nbn:se:umu:diva-124162 (URN)10.1093/philmat/nkw015 (DOI)000439703300003 ()2-s2.0-85053033011 (Scopus ID)
Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2018-11-01Bibliographically approved
Öhman, L.-D. (2016). A Beautiful Proof by Induction. Journal of Humanistic Mathematics, 6(1), 73-85
Open this publication in new window or tab >>A Beautiful Proof by Induction
2016 (English)In: Journal of Humanistic Mathematics, ISSN 2159-8118, E-ISSN 2159-8118, Vol. 6, no 1, p. 73-85Article in journal (Refereed) Published
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.

National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-118552 (URN)10.5642/jhummath.201601.06 (DOI)000388610000005 ()
Available from: 2016-03-23 Created: 2016-03-23 Last updated: 2018-06-07Bibliographically approved
Raman-Sundström, M., Öhman, L.-D. & Sinclair, N. (2016). The Nature and Experience of Mathematical Beauty (1ed.). Journal of Humanistic Mathematics, 6(1), 3-7
Open this publication in new window or tab >>The Nature and Experience of Mathematical Beauty
2016 (English)In: Journal of Humanistic Mathematics, ISSN 2159-8118, E-ISSN 2159-8118, Vol. 6, no 1, p. 3-7Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Claremont, CA, USA: , 2016 Edition: 1
National Category
Philosophy Other Mathematics
Research subject
Mathematics; Aesthetics
Identifiers
urn:nbn:se:umu:diva-115217 (URN)10.5642/jhummath.201601.03 (DOI)000388610000002 ()
Projects
Karriärbidrag
Available from: 2016-02-01 Created: 2016-02-01 Last updated: 2018-06-07Bibliographically approved
Raman Sundström, M. & Öhman, L.-D. (2015). Mathematical fit: A first approximation. In: Krainer, K Vondrova, N (Ed.), Proceedings of the ninth conference of the Euorpean Society for research in Mathermatics education (CERME9): . Paper presented at 9th Congress of European Research in Mathematics Education, Prague, February 4-8, 2015. (pp. 185-191). Prague: Charles University
Open this publication in new window or tab >>Mathematical fit: A first approximation
2015 (English)In: Proceedings of the ninth conference of the Euorpean Society for research in Mathermatics education (CERME9) / [ed] Krainer, K Vondrova, N, Prague: Charles University , 2015, p. 185-191Conference paper, Oral presentation with published abstract (Refereed)
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.

Place, publisher, year, edition, pages
Prague: Charles University, 2015
Keywords
Proof, fit, explanation, beauty, aesthetics
National Category
Mathematics Learning
Identifiers
urn:nbn:se:umu:diva-163260 (URN)000466853900021 ()978-80-7290-844-8 (ISBN)
Conference
9th Congress of European Research in Mathematics Education, Prague, February 4-8, 2015.
Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-18Bibliographically approved
Shcherbak, D., Jäger, G. & Öhman, L.-D. (2015). The Zero Forcing Number of Bijection Graphs. In: Proceedings of 26th International Workshop om Combinatorial Algorithms (IWOCA 2015): . Paper presented at 26th International Workshop om Combinatorial Algorithms (IWOCA 2015), Verona, Italy, October 5-7, 2015 (pp. 334-345). Berlin-Heidelberg: Springer, 9538
Open this publication in new window or tab >>The Zero Forcing Number of Bijection Graphs
2015 (English)In: Proceedings of 26th International Workshop om Combinatorial Algorithms (IWOCA 2015), Berlin-Heidelberg: Springer, 2015, Vol. 9538, p. 334-345Conference paper, Published paper (Refereed)
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)≥δ(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.

Place, publisher, year, edition, pages
Berlin-Heidelberg: Springer, 2015
Series
Lecture Notes in Computer Science ; 9538
Keywords
Zero forcing set, Zero forcing number, Bijection graph
National Category
Discrete Mathematics
Identifiers
urn:nbn:se:umu:diva-125915 (URN)10.1007/978-3-319-29516-9_28 (DOI)978-3-319-29515-2 (ISBN)978-3-319-29516-9 (ISBN)
Conference
26th International Workshop om Combinatorial Algorithms (IWOCA 2015), Verona, Italy, October 5-7, 2015
Available from: 2016-09-22 Created: 2016-09-22 Last updated: 2019-06-26Bibliographically approved
Nilson, T. & Öhman, L.-D. (2015). Triple arrays and Youden squares. Designs, Codes and Cryptography, 75(3), 429-451
Open this publication in new window or tab >>Triple arrays and Youden squares
2015 (English)In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 75, no 3, p. 429-451Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2015
Keywords
triple array, double array, Youden square, difference set, SBIBD
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-92724 (URN)10.1007/s10623-014-9926-8 (DOI)000353059700005 ()
Available from: 2014-09-01 Created: 2014-09-01 Last updated: 2018-06-07Bibliographically approved
Denley, T. & Öhman, L.-D. (2014). Extending partial latin cubes. Ars combinatoria, 113, 405-414
Open this publication in new window or tab >>Extending partial latin cubes
2014 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 113, p. 405-414Article in journal (Refereed) Published
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.

National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-50292 (URN)000329883500036 ()
Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2018-06-08Bibliographically approved
Andren, L. J., Casselgren, C. J. & Öhman, L.-D. (2013). Avoiding Arrays of Odd Order by Latin Squares. Combinatorics, probability & computing, 22(2), 184-212
Open this publication in new window or tab >>Avoiding Arrays of Odd Order by Latin Squares
2013 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 22, no 2, p. 184-212Article in journal (Refereed) Published
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.

National Category
Discrete Mathematics
Identifiers
urn:nbn:se:umu:diva-66768 (URN)10.1017/S0963548312000570 (DOI)000314296400002 ()
Available from: 2013-03-15 Created: 2013-03-05 Last updated: 2018-06-08Bibliographically approved
Raman Sundström, M. & Öhman, L.-D. (2013). Beauty as fit: A metaphor in mathematics?. Research in Mathematics Education, 15(2), 199-200
Open this publication in new window or tab >>Beauty as fit: A metaphor in mathematics?
2013 (English)In: Research in Mathematics Education, Vol. 15, no 2, p. 199-200Article in journal (Refereed) Published
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.

Keywords
Beauty, aesthetics, mathematics
National Category
Other Mathematics Philosophy
Research subject
Aesthetics
Identifiers
urn:nbn:se:umu:diva-98062 (URN)10.1080/14794802.2013.797740 (DOI)
Projects
Karriärbidrag on Beauty in Mathematics, Umeå University
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2018-06-07Bibliographically approved
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