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
SN - 1063-8539
VL - 20
SP - 227
EP - 263
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
IS - 5
ER -