A congruence connecting Latin rectangles and partial orthomorphisms

DOI10.1007/s00026-012-0137-6zbMath1256.05030OpenAlexW1986001904MaRDI QIDQ1928590

Rebecca J. Stones, Ian M. Wanless

Publication date: 3 January 2013

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00026-012-0137-6

zbMATH Keywords

Latin squareorthomorphismLatin rectanglepartial orthomorphismPORC function

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Orthogonal arrays, Latin squares, Room squares (05B15) Coloring of graphs and hypergraphs (05C15) Sequences (mod (m)) (11B50)

Related Items (10)

Hownotto prove the Alon-Tarsi conjecture ⋮ On computing the number of Latin rectangles ⋮ Cycle structure of autotopisms of quasigroups and latin squares ⋮ Partial Latin rectangle graphs and autoparatopism groups of partial Latin rectangles with trivial autotopism groups ⋮ The set of autotopisms of partial Latin squares ⋮ Enumerating partial Latin rectangles ⋮ Bounds on the number of autotopisms and subsquares of a Latin square ⋮ On the number of transversals in Cayley tables of cyclic groups ⋮ Compound orthomorphisms of the cyclic group ⋮ Symmetries of partial Latin squares

Uses Software

• OEIS

Cites Work

• The parity of the number of quasigroups
• The number of transversals in a Latin square
• Applying fast simulation to find the number of good permutations
• Divisors of the number of Latin rectangles
• On the number of transversals in Cayley tables of cyclic groups
• Compound orthomorphisms of the cyclic group
• The many formulae for the number of Latin rectangles
• Estimating the number of good permutations by a modified fast simulation method
• The spectrum for quasigroups with cyclic automorphisms and additional symmetries.
• Estimating the number of Latin rectangles by the fast simulation method
• Diagonally cyclic Latin squares.
• Calculation of the number of complete mappings for permutations
• Latin squares of order 10
• Bounds on the number of autotopisms and subsquares of a Latin square
• On the number of Latin squares
• Hownotto prove the Alon-Tarsi conjecture
• Small latin squares, quasigroups, and loops
• ON THE NUMBER OF LATIN RECTANGLES
• Systems Of Linear Congruences
• Orthomorphism graphs of groups
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