The spectrum for quasigroups with cyclic automorphisms and additional symmetries.

DOI10.1016/j.disc.2008.01.020zbMath1221.20047OpenAlexW1971236443MaRDI QIDQ1011718

Melinda Buchanan, Ian M. Wanless, Darryn E. Bryant

Publication date: 9 April 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2008.01.020

zbMATH Keywords

Latin squaresSteiner triple systemsMendelsohn triple systemsfinite quasigroupscyclic automorphismssemi-symmetric quasigroupsspectrum of quasigroupstotally symmetric quasigroups

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15) Loops, quasigroups (20N05) Triple systems (05B07)

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Cycle structure of autotopisms of quasigroups and latin squares ⋮ The set of autotopisms of partial Latin squares ⋮ A congruence connecting Latin rectangles and partial orthomorphisms ⋮ Autoparatopisms of Quasigroups and Latin Squares ⋮ Computing Autotopism Groups of Partial Latin Rectangles ⋮ Enumerating partial Latin rectangles ⋮ Enumeration of Latin squares with conjugate symmetry ⋮ Lambda-rings of automorphisms ⋮ Diagonally cyclic Latin squares. ⋮ Diagonally cyclic equitable rectangles ⋮ ON THE NUMBER OF LATIN RECTANGLES ⋮ Quasigroup automorphisms and the Norton-Stein complex ⋮ New families of atomic Latin squares and perfect 1-factorisations. ⋮ Autotopism stabilized colouring games on rook's graphs ⋮ Colouring games based on autotopisms of Latin hyper-rectangles ⋮ Symmetries of partial Latin squares ⋮ Refining invariants for computing autotopism groups of partial Latin rectangles ⋮ Lagrange's theorem for Hom-groups ⋮ The Order of Automorphisms of Quasigroups

Cites Work

• Steiner triple systems with rotational automorphisms
• Sequencings and starters
• Hooked \(k\)-extended Skolem sequences
• Diagonally cyclic Latin squares.
• Extended triple systems
• On certain distributions of integers in pairs with given differences
• Verification of a Conjecture of Th. Skolem.
• Extended skolem sequences
• Decompositions of complete graphs into triangles and Hamilton cycles
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