The number of Latin squares of order 11

DOI10.1090/S0025-5718-2010-02420-2zbMath1210.05017arXiv0909.3402MaRDI QIDQ3168748

Patric R. J. Östergård, Alexander Hulpke, Petteri Kaski

Publication date: 19 April 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3402

zbMATH Keywords

enumerationLatin squareMain class

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Orthogonal arrays, Latin squares, Room squares (05B15) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (31)

A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five ⋮ A new algorithm for enumerating all possible Sudoku squares ⋮ Cycle structure of autotopisms of quasigroups and latin squares ⋮ Classifying partial Latin rectangles ⋮ Unnamed Item ⋮ Partial Latin rectangle graphs and autoparatopism groups of partial Latin rectangles with trivial autotopism groups ⋮ Enumerating perfect matchings in \(n\)-cubes ⋮ The set of autotopisms of partial Latin squares ⋮ Autoparatopisms of Quasigroups and Latin Squares ⋮ Computing Autotopism Groups of Partial Latin Rectangles ⋮ Enumerating partial Latin rectangles ⋮ Enumerating Steiner triple systems ⋮ Steiner triple systems of order 21 with a transversal subdesign \(\mathrm{TD}(3, 6)\) ⋮ Cocyclic Hadamard matrices over Latin rectangles ⋮ What (Quilting) Circles Can Be Squared? ⋮ A computational approach to analyze the Hadamard quasigroup product ⋮ The number of labeled \(n\)-ary abelian groups and totally symmetric medial quasigroups ⋮ 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 ⋮ Autotopism stabilized colouring games on rook's graphs ⋮ Enumeration of MOLS of small order ⋮ Colouring games based on autotopisms of Latin hyper-rectangles ⋮ Symmetries of partial Latin squares ⋮ Isotopy graphs of Latin tableaux ⋮ A computational algebraic geometry approach to analyze pseudo-random sequences based on Latin squares ⋮ Using a CAS/DGS to analyze computationally the configuration of planar bar linkage mechanisms based on partial Latin squares ⋮ The Order of Automorphisms of Quasigroups ⋮ Enumeration of Steiner triple systems with subsystems ⋮ A historical perspective of the theory of isotopisms ⋮ Counting Hamiltonian cycles in bipartite graphs

Uses Software

• GAP
• gmp
• nauty
• libexact

Cites Work

• Unnamed Item
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• Classification algorithms for codes and designs
• On the number of 8\(\times 8\) Latin squares
• Divisors of the number of Latin rectangles
• On the number of Latin squares
• Small latin squares, quasigroups, and loops
• There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations ofK₁₄
• Isomorph-Free Exhaustive Generation
• There are 526,915,620 nonisomorphic one‐factorizations of K₁₂
• Isomorph-Free Exhaustive Generation of Designs with Prescribed Groups of Automorphisms
• THE 7 × 7 SQUARES
• An Omission in Norton's List of $7 \times 7$ Squares

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