Further Results on Latin Squares with Disjoint Subsquares using Rational Outline Squares

2025/05/12 by Tara Kemp, Kemp, Tara, James Lefevre +1 · 1 voice · 1 citation
Computer Science · Engineering · Mathematics · #Graph Labeling and Dimension Problems #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.37236/14201

openalex created_date 2025/11/13 · openalex publication_date 2025/11/13 · openalex updated_date 2026/07/31

Abstract

In this paper we consider the problem of finding latin squares with sets of pairwise disjoint subsquares. We develop a new necessary condition on the sizes of the subsquares which incorporates and extends the known conditions. We provide a construction for the case where all but two of the subsquares are the same size, and in this case the condition is sufficient. We obtain these results using symmetric rational outline squares, and additionally provide several new results and extensions to this theory.

Citations

• Subsquares in random Latin rectangles
• Canonical labelling of Latin squares in average-case polynomial time
• Latin squares without proper subsquares

Cited by

• Latin squares with three disjoint subsquares of the same order

Discussions

• 📢 New publication 'Further Results on Latin Squares with Disjoint Subsquares using Rational Outline Squares' by Tara Kemp and James Lefevre in The Electronic Journal of Combinatorics 🧮🧪 #LatinSqua [bsky, 2 points, 0 comments]

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