Latin cubes with disjoint subcubes of two orders

2025/11/10 by Tara Kemp, Kemp, Tara, James Lefevre +2 · 1 voice
Engineering · Mathematics · #Finite Group Theory Research #Mathematics and Applications #graph theory and CDMA systems

paper · doi:10.1016/j.disc.2026.115128

openalex publication_date 2026/03/24 · openalex created_date 2026/03/25 · openalex updated_date 2026/03/25

Abstract

Given a partition h₁+h₂+…+h_k = n, a latin square of order n with pairwise disjoint subsquares of orders h₁,… ,h_k is called a realization. When the values h_i are of at most two sizes, the existence of a realization has been completely determined. However, the existence of a latin cube with pairwise disjoint subcubes of two orders is only partially solved. In this paper, we determine existence for such latin cubes in almost all cases.

Discussions

• 📢 New publication 'Latin cubes with disjoint subcubes of two orders' by Tara Kemp and James Lefevre in Discrete Mathematics 🧮🧪 #LatinSquare #PermutationCube #Realization doi.org/10.1016/j.di... [bsky, 2 points, 0 comments]

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