Latin hypercubes realizing integer partitions
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.
Authors
- James Lefevre (ORCID: https://orcid.org/0000-0002-5945-9575)
- Diane Donovan (ORCID: https://orcid.org/0000-0002-1329-3514)
- Tara Kemp (ORCID: https://orcid.org/0009-0001-7371-8705)
Institutions
- ARC Centre of Excellence for Plant Success in Nature and Agriculture (AU)
Publication Details
- Journal
- Discrete Mathematics
- Published
- 2024-11-26
- DOI
- https://doi.org/10.1016/j.disc.2024.114333
- Citations
- 2
- Primary Topic
- graph theory and CDMA systems
- Type
- article
- Field-Weighted Citation Impact
- 0.42
Funders
- Australian Government
- Australian Research Council
- Australian Research Council Centre of Excellence for Plant Success in Nature and Agriculture