TY - JOUR

T1 - Cycle structure of autotopisms of quasigroups and Latin squares

AU - Stones, Douglas Stuart

AU - Vojtechovsky, Petr

AU - Wanless, Ian Murray

PY - 2012

Y1 - 2012

N2 - An autotopism of a Latin square is a triple (alpha, beta, gamma) of permutations such that the Latin square is mapped to itself by permuting its rows by alpha, columns by beta, and symbols by gamma. Let Atp(n) be the set of all autotopisms of Latin squares of order n. Whether a triple (alpha, beta, gamma) of permutations belongs to Atp(n) depends only on the cycle structures of alpha, beta, and gamma. We establish a number of necessary conditions for (alpha, beta, gamma) to be in Atp(n), and use them to determine Atp(n) for n

AB - An autotopism of a Latin square is a triple (alpha, beta, gamma) of permutations such that the Latin square is mapped to itself by permuting its rows by alpha, columns by beta, and symbols by gamma. Let Atp(n) be the set of all autotopisms of Latin squares of order n. Whether a triple (alpha, beta, gamma) of permutations belongs to Atp(n) depends only on the cycle structures of alpha, beta, and gamma. We establish a number of necessary conditions for (alpha, beta, gamma) to be in Atp(n), and use them to determine Atp(n) for n

UR - http://onlinelibrary.wiley.com/doi/10.1002/jcd.20309/abstract;jsessionid=183F5B6C2078413EC8F2F62DA019F4C7.d01t04

U2 - 10.1002/jcd.20309

DO - 10.1002/jcd.20309

M3 - Article

VL - 20

SP - 227

EP - 263

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

SN - 1063-8539

IS - 5

ER -