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arXiv · 2511.06768

Latin cubes with disjoint subcubes of two orders

Tara Kemp·James G. Lefevre
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Abstract

Given a partition $h_1+h_2+\dots+h_k = n$, a latin square of order $n$ with pairwise disjoint subsquares of orders $h_1,\dots ,h_k$ 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.

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Tara Kemp, James G. Lefevre. 2025-11-10. Latin cubes with disjoint subcubes of two orders. https://doi.org/10.1016/j.disc.2026.115128

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