Latin cubes with disjoint subcubes of two orders
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.
Fields of Study & Subjects
graph theory and CDMA systems
Finite Group Theory Research
Mathematics and Applications
Publication details
- Journal / source
- Discrete Mathematics
- Volume
- 349
- Issue
- 8
- Pages
- 115128–115128
- Publication date
- 24 March 2026
- Language
- EN