Cycle structure of autotopisms of quasigroups and latin squares

DOI10.1002/jcd.20309zbMath1248.05023arXiv1509.05655OpenAlexW1911411026MaRDI QIDQ2909597

Petr Vojtěchovský, Ian M. Wanless, Rebecca J. Stones

Publication date: 30 August 2012

Published in: Journal of Combinatorial Designs (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05655

zbMATH Keywords

automorphismquasigroupLatin squarecycle structureautotopismdiagonally cyclic Latin square

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items (23)

A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five ⋮ On computing the number of Latin rectangles ⋮ A Latin square autotopism secret sharing scheme ⋮ Homotopies of Central Quasigroups ⋮ Classifying partial Latin rectangles ⋮ Partial Latin rectangle graphs and autoparatopism groups of partial Latin rectangles with trivial autotopism groups ⋮ The set of autotopisms of partial Latin squares ⋮ Autoparatopisms of Quasigroups and Latin Squares ⋮ Computing the autotopy group of a Latin square by cycle structure ⋮ Computing Autotopism Groups of Partial Latin Rectangles ⋮ Enumerating partial Latin rectangles ⋮ Enumeration of Latin squares with conjugate symmetry ⋮ Bounds on the number of autotopisms and subsquares of a Latin square ⋮ Diagonally cyclic equitable rectangles ⋮ Autotopism stabilized colouring games on rook's graphs ⋮ Colouring games based on autotopisms of Latin hyper-rectangles ⋮ Symmetries of partial Latin squares ⋮ Autoparatopism stabilized colouring games on rook's graphs ⋮ Permanents and Determinants of Latin Squares ⋮ Latin Squares with a Unique Intercalate ⋮ Refining invariants for computing autotopism groups of partial Latin rectangles ⋮ The Order of Automorphisms of Quasigroups ⋮ A historical perspective of the theory of isotopisms

Uses Software

• GAP
• nauty
• LOOPS

Cites Work

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• BUCHSTEINER LOOPS
• Small latin squares, quasigroups, and loops
• Latin squares with no small odd plexes
• A Class of Loops Which are Isomorphic to all Loop Isotopes
• Simple Moufang loops
• Symmetries that latin squares inherit from 1‐factorizations
• Quasigroup automorphisms and the Norton-Stein complex
• Computing with small quasigroups and loops

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