# Equivalence classes of critical sets based on non-trivial autotopisms of Latin squares

Published: 14 August 2020| Version 1 | DOI: 10.17632/fkm575299m.1
Contributors:
Raul Falcon Ganfornina,
Laura Johnson,
Stephanie Perkins

## Description

Census of equivalence classes of critical sets based on non-trivial autotopisms of Latin squares. Each file is labeled as X_A_B_C_D.txt, where * X refers to the main class of the Latin square; * (A,B,C) refers to the cycle structure of the autotopism; * D refers to the corresponding result or example in the paper Johnson, L., Falcón, R. M., Perkins, S. "A census of Theta-critical sets based on autotopisms of Latin squares of order up to five". Submitted, 2020. Thus, for instance, the file L52_221_221_221_Example_34.txt refers to an autotopism of the Latin square \$L_{5.2}\$, with cycle structure \$(2^21,2^21,2^21)\$, which is illustrated in Example 34 in the mentioned paper. In any case, an illustrative example of Latin square and autotopism is indicated in the description of each file. In each file, each partial Latin square is written row by row in a unique line. Empty entries are represented by zeros. Thus, for instance, the partial Latin square 1 * 3 * 2 * 2 1 * is represented as 103020210

## Institutions

Universidad de Sevilla, University of South Wales

Combinatorics