Latin cubes with disjoint subcubes of two orders

Abstract

Given a partition $h_1+h_2+\cdots +h_k=n$, 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.

References in corpus (1)

• Latin hypercubes realizing integer partitions