Every latin hypercube of order 5 has transversals

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 $n\ge 3$ and $q\ge 3$ 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.

Supplementary data https://zenodo.org/records/10204026

References in corpus (1)

• Transversals in quasirandom latin squares

Cited by in corpus (1)

• Characterization of polystochastic matrices of order $4$ with zero permanent