arXiv Open Access 2023

Every latin hypercube of order 5 has transversals

A. L. Perezhogin V. N. Potapov S. Yu. Vladimirov

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.CO cs.IT

Penulis (3)

A. L. Perezhogin

V. N. Potapov

S. Yu. Vladimirov

Format Sitasi

APA MLA BibTeX

Perezhogin, A.L., Potapov, V.N., Vladimirov, S.Y. (2023). Every latin hypercube of order 5 has transversals. https://arxiv.org/abs/2311.14997

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓