Realizations with five subsquares
Abstract
Given an integer partition $(h_1,h_2,\dots,h_k)$ of $n$, is it possible to find an order $n$ latin square with $k$ disjoint subsquares of orders $h_1,\dots,h_k$? This question was posed by L.Fuchs and is only partially solved. Existence has been determined in general when $k\leq 4$, and in this paper we will complete the case when $k=5$. We also prove some less general results for partitions with $k=5$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.00967
- arXiv:
- arXiv:2406.00967
- Bibcode:
- 2024arXiv240600967K
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 15 pages, 17 figures