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Öhman, Lars-Daniel

Open this publication in new window or tab >>Triples of Orthogonal Latin and Youden Rectangles of small order### Jäger, Gerold

### Markström, Klas

### Öhman, Lars-Daniel

### Shcherbak, Denys

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-158857 (URN)10.1002/jcd.21642 (DOI)000459040800001 ()2-s2.0-85059030594 (PubMedID)
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Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-23Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.

Open this publication in new window or tab >>Mathematical fit: a case study### Raman-Sundström, Manya

### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2018-11-01Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

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.

Open this publication in new window or tab >>A Beautiful Proof by Induction### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### National Category

Other Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-118552 (URN)10.5642/jhummath.201601.06 (DOI)000388610000005 ()
#####

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Available from: 2016-03-23 Created: 2016-03-23 Last updated: 2018-06-07Bibliographically approved

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.

Open this publication in new window or tab >>The Nature and Experience of Mathematical Beauty### Raman-Sundström, Manya

### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Sinclair, Nathalie

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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##### Projects

Karriärbidrag
Available from: 2016-02-01 Created: 2016-02-01 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Faculty of Education, Simon Fraser University, CANADA.

Open this publication in new window or tab >>Mathematical fit: A first approximation### Raman Sundström, Manya

### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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.
#####

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Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-18Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

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.

Open this publication in new window or tab >>The Zero Forcing Number of Bijection Graphs### Shcherbak, Denys

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Jäger, Gerold

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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]

##### 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
#####

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Available from: 2016-09-22 Created: 2016-09-22 Last updated: 2019-06-26Bibliographically approved

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 2*n* 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.

Open this publication in new window or tab >>Triple arrays and Youden squares### Nilson, Tomas

### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
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Available from: 2014-09-01 Created: 2014-09-01 Last updated: 2018-06-07Bibliographically approved

Mittuniversitetet.

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.

Open this publication in new window or tab >>Extending partial latin cubes### Denley, Tristan

### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 113, p. 405-414Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-50292 (URN)000329883500036 ()
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Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2018-06-08Bibliographically approved

Austin Peay State University.

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.

Open this publication in new window or tab >>Avoiding Arrays of Odd Order by Latin Squares### Andren, Lina J.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Casselgren, Carl Johan

### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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]

##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-66768 (URN)10.1017/S0963548312000570 (DOI)000314296400002 ()
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Available from: 2013-03-15 Created: 2013-03-05 Last updated: 2018-06-08Bibliographically approved

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.

Open this publication in new window or tab >>Beauty as fit: A metaphor in mathematics?### Raman Sundström, Manya

### Öhman, Lars-Daniel

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##### Abstract [en]

##### 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)
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##### Projects

Karriärbidrag on Beauty in Mathematics, Umeå University
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.