Autoparatopisms of Quasigroups and Latin Squares | Zendy

Mendis Mahamendige Jayama Lalani | Zendy; Wanless Ian M. | Zendy

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Autoparatopisms of Quasigroups and Latin Squares

Author(s) -

Mendis Mahamendige Jayama Lalani,

Wanless Ian M.

Publication year - 2017

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21515

Subject(s) - latin square , mathematics , combinatorics , square (algebra) , wreath product , order (exchange) , set (abstract data type) , product (mathematics) , quasigroup , geometry , computer science , rumen , chemistry , food science , finance , fermentation , economics , programming language

Paratopism is a well‐known action of the wreath productS n ≀ S 3on Latin squares of order n . A paratopism that maps a Latin square to itself is an autoparatopism of that Latin square. Let Par( n ) denote the set of paratopisms that are an autoparatopism of at least one Latin square of order n . We prove a number of general properties of autoparatopisms. Applying these results, we determine Par( n ) for n ⩽ 17 . We also study the proportion of all paratopisms that are in Par( n ) as n → ∞ .

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