Geodesic
Further Results on Latin Squares with Disjoint Subsquares using Rational Outline Squares
Tara Kemp1 ; James G. Lefevre1
1University of Queensland
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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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.
DOI : 10.37236/14201

Tara Kemp  1   ; James G. Lefevre  1

1 University of Queensland 
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     author = {Tara Kemp and James G. Lefevre},
     title = {Further {Results} on {Latin} {Squares} with {Disjoint} {Subsquares} using {Rational} {Outline} {Squares}},
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Tara Kemp; James G. Lefevre. Further Results on Latin Squares with Disjoint Subsquares using Rational Outline Squares. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/14201

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