Work

Latin hypercubes realizing integer partitions

Year: 2024

Type: article

Abstract: For an integer partition h 1 + … + h n = N , a 2-realization of this partition is a latin square of order N with disjoint subsquares of orders h 1 , … , h n . The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to m -ary quasigroups, or, equivalently, latin hypercubes. We construct latin cubes for some partitions with at most two distinct parts and highlight how the new problem is related to the original.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2024.114333

Authors: Diane Donovan, Tara Kemp, James Lefevre

Institutions: The University of Queensland, ARC Centre of Excellence for Plant Success in Nature and Agriculture

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,120

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