Every latin hypercube of order 5 has transversals Full article
| Journal |
Journal of Combinatorial Designs
ISSN: 1063-8539 |
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| Output data | Year: 2024, Volume: 32, Number: 11, Pages: 679-699 Pages count : 21 DOI: 10.1002/jcd.21954 | ||||||
| Tags | latin hypercube, latin square, nonextendible latin cuboid, permanent of multidimensional matrix, transversal | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
We prove that for all n > 1 every latin n‐dimensional cube of order 5 has transversals. We find all 123 paratopy classes of layer‐latin cubes of order 5 with no transversals. For each ≥ n 3and ≥ q q q ⋯ latin square of order q is aq q q 3weconstruct a (2 − 2) × × × latin n‐dimensional cuboid of order q with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5.
Cite:
Perezhogin A.L.
, Potapov V.N.
, Vladimirov S.Y.
Every latin hypercube of order 5 has transversals
Journal of Combinatorial Designs. 2024. V.32. N11. P.679-699. DOI: 10.1002/jcd.21954 WOS Scopus РИНЦ OpenAlex
Every latin hypercube of order 5 has transversals
Journal of Combinatorial Designs. 2024. V.32. N11. P.679-699. DOI: 10.1002/jcd.21954 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Nov 25, 2023 |
| Accepted: | Jul 15, 2024 |
| Published print: | Jul 30, 2024 |
| Published online: | Jul 30, 2024 |
Identifiers:
| Web of science: | WOS:001281441800001 |
| Scopus: | 2-s2.0-85200028211 |
| Elibrary: | 69039729 |
| OpenAlex: | W4401131688 |