Work

Latin cubes with disjoint subcubes of two orders

Year: 2026

Type: article

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.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2026.115128

Authors: Tara Kemp, James G. Lefevre

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: Australian Government, Government of Western Australia, Australian Research Council, Australian Research Council Centre of Excellence for Plant Success in Nature and Agriculture

Awards: ARC Centre of Excellence for Plant Success in Nature and Agriculture, G80507876