arXiv
Open Access
2026
Latin squares with non-partitioning disjoint subsquares
Tara Kemp
Abstrak
A latin square of order $n$ with pairwise disjoint subsquares of orders $h_1,\dots,h_k$ such that $h_1+\dots+h_k = n$ is known as a realization. The existence of realizations is a partially solved problem with a few general results for an arbitrary number of subsquares, $k$. Requiring only that $h_1+\dots+h_k\leq n$ gives a variation of the problem that has few known results. In this paper we prove a general necessary condition for existence and completely determine existence when there are at most three subsquares or the subsquares are all of the same order. Importantly, we prove that if $h_1\geq h_2\geq\dots\geq h_k$ and $n\geq h_1+\sum_{i=1}^kh_i$ then such a latin square always exists.
Topik & Kata Kunci
Penulis (1)
T
Tara Kemp
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2026
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓