Every latin hypercube of order 5 has transversals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909927157530624 |
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| author | Perezhogin, A. L. Potapov, V. N. Vladimirov, S. Yu. |
| author_facet | Perezhogin, A. L. Potapov, V. N. Vladimirov, S. Yu. |
| contents | 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 $n\geq 3$ and $q\geq 3$ we construct a (2q-2)-layer latin n-dimensional cuboid with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_14997 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Every latin hypercube of order 5 has transversals Perezhogin, A. L. Potapov, V. N. Vladimirov, S. Yu. Combinatorics Information Theory 05B15 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 $n\geq 3$ and $q\geq 3$ we construct a (2q-2)-layer latin n-dimensional cuboid with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5. |
| title | Every latin hypercube of order 5 has transversals |
| topic | Combinatorics Information Theory 05B15 |
| url | https://arxiv.org/abs/2311.14997 |