arXiv Open Access 2025

Latin squares with three disjoint subsquares of the same order

Tara Kemp James G. Lefevre

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Abstrak

Given an integer partition $P = (h_1h_2\dots h_k)$ of $n$, a realization of $P$ is a latin square with disjoint subsquares of orders $h_1,h_2,\dots,h_k$. Most known results restrict either $k$ or the number of different integers in $P$. There is little known for partitions with arbitrary $k$ and subsquares of at least three orders. It has been conjectured that if $h_1=h_2=h_3\geq h_4\geq\dots\geq h_k$ then a realization of $P$ always exists. We prove this conjecture, and thus show the existence of realizations for many general partitions.

Topik & Kata Kunci

math.CO

Penulis (2)

Tara Kemp

James G. Lefevre

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APA MLA BibTeX

Kemp, T., Lefevre, J.G. (2025). Latin squares with three disjoint subsquares of the same order. https://arxiv.org/abs/2510.00364

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓