ON THE NUMBER OF LATIN RECTANGLES

DOI10.1017/S0004972710000328zbMath1200.05041OpenAlexW1981469958MaRDI QIDQ3580003

Rebecca J. Stones

Publication date: 11 August 2010

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972710000328

zbMATH Keywords

automorphismquasigroupLatin squareorthomorphismLatin rectangleautotopismAlon-Tarsi conjecture

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Orthogonal arrays, Latin squares, Room squares (05B15) Automorphisms of abstract finite groups (20D45) Sequences (mod (m)) (11B50)

Related Items (9)

On computing the number of Latin rectangles ⋮ A Latin square autotopism secret sharing scheme ⋮ A congruence connecting Latin rectangles and partial orthomorphisms ⋮ Enumerating partial Latin rectangles ⋮ Bounds on the number of autotopisms and subsquares of a Latin square ⋮ Eigenproblems of Latin squares in bipartite \((\min, \max,+)\)-systems ⋮ The parity of the number of quasigroups ⋮ Symmetries of partial Latin squares ⋮ The Alon-Tarsi conjecture: a perspective on the main results

Cites Work

• Divisors of the number of Latin rectangles
• Compound orthomorphisms of the cyclic group
• The spectrum for quasigroups with cyclic automorphisms and additional symmetries.
• Colorings and orientations of graphs
• On the number of even and odd Latin squares of order \(p+1\)
• Diagonally cyclic Latin squares.
• On the number of Latin squares
• Small latin squares, quasigroups, and loops
• A Recurrence Relation for Three-Line Latin Rectangles
• Orthomorphism graphs of groups

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