On Parity Vectors of Latin Squares

被引:1
作者
Donovan, D. M. [1 ]
Grannell, M. J. [2 ]
Griggs, T. S. [2 ]
Lefevre, J. G. [1 ]
机构
[1] Univ Queensland, Ctr Discrete Math & Comp, St Lucia, Qld 4072, Australia
[2] Open Univ, Dept Math & Stat, Milton Keynes MK7 6AA, Bucks, England
基金
澳大利亚研究理事会;
关键词
Latin square; Orientable surface; Biembedding; Parity vector; Group; Steiner quasigroup; Steiner loop; BIEMBEDDINGS;
D O I
10.1007/s00373-010-0942-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The parity vectors of two Latin squares of the same side n provide a necessary condition for the two squares to be biembeddable in an orientable surface. We investigate constraints on the parity vector of a Latin square resulting from structural properties of the square, and show how the parity vector of a direct product may be obtained from the parity vectors of the constituent factors. Parity vectors for Cayley tables of all Abelian groups, some non-Abelian groups, Steiner quasigroups and Steiner loops are determined. Finally, we give a lower bound on the number of main classes of Latin squares of side n that admit no self-embeddings.
引用
收藏
页码:673 / 684
页数:12
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