Perezhogin, Alexey L. and Potapov, Vladimir N. and Vladimirov, Sergey Yu (2024) Every latin hypercube of order 5 has transversals. Journal of Combinatorial Designs . ISSN 1063-8539 (Print) 1520-6610 (Online) Published Online First https://dx.doi.org/10.1002/jcd.21954
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Official URL: https://dx.doi.org/10.1002/jcd.21954
Abstract
We prove that for all (Formula presented.) every latin (Formula presented.) -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 (Formula presented.) and (Formula presented.) we construct a (Formula presented.) latin (Formula presented.) -dimensional cuboid of order (Formula presented.) with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | latin hypercube; latin square; nonextendible latin cuboid; permanent of multidimensional matrix; transversal |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | IC-Cataloging |
| Date Deposited: | 23 Aug 2024 16:14 |
| Last Modified: | 23 Aug 2024 16:14 |
| URI: | https://research.sabanciuniv.edu/id/eprint/49790 |
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