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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.10981 |
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Table of Contents:
- For an integer partition $h_1 + \dots + h_n = N$, a 2-realization of this partition is a latin square of order $N$ with disjoint subsquares of orders $h_1,\dots,h_n$. 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.