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Triples of Orthogonal Latin and Youden Rectangles of small order
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.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
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.

Place, publisher, year, edition, pages
2019. Vol. 27, no 4, p. 229-250
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-158857DOI: 10.1002/jcd.21642ISI: 000459040800001PubMedID: 2-s2.0-85059030594OAI: oai:DiVA.org:umu-158857DiVA, id: diva2:1315240
Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-23Bibliographically approved
In thesis
1. Enumerative approaches and structural results for selected combinatorial problems
Open this publication in new window or tab >>Enumerative approaches and structural results for selected combinatorial problems
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå University, 2019. p. 8
Keywords
Graph, zero forcing, Latin squares, Youden squares, designs
National Category
Discrete Mathematics Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-158865 (URN)978-91-7855-086-9 (ISBN)
Public defence
2019-06-14, MA121, 10:00 (English)
Opponent
Supervisors
Available from: 2019-05-24 Created: 2019-05-23 Last updated: 2019-05-24Bibliographically approved

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Jäger, GeroldMarkström, KlasÖhman, Lars-DanielShcherbak, Denys

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