On the Number of Latin Squares
By Brendan D. McKay, Ian M. Wanless. 2005
191 citations recorded by the source corpus.
Abstract.We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, (2) answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by f! where f is a particular integer close to $$\frac{1}{2}n,$$ (3) provide a formula for the number of Latin squares in terms of permanents of (+1, −1)-matrices, (4) find the extremal values for the number of 1-factorisations of k-regular bipartite graphs on 2n vertices whenever 1 ≤ k ≤ n ≤ 11, (5) show that the proportion of Latin squares with a non-trivial symmetry group tends quickly to zero as the order increases.
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/f9040d02d57b3d7b42feb4937c0dfb1e65a9eff5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Computational Theory and Mathematics
- Wendy J. Myrvold
- Alison M. Meynert
- Nicholas J. Cavenagh
- Brendan D. McKay
- Nicholas A. Cook
- Charles Bordenave
In Electrical and Electronic Engineering
Citations in the corpus
- The theory and application of latin bitrades: A survey (2008, background): “However, M c K a y and W a n l e s s [55] recently showed that the number of latin squares of order 11 is:”
- Small latin squares, quasigroups, and loops (2007, methodology): “The number of reduced squares was obtained for order 9 by Bammel and Rothstein [4], for order 10 by McKay and Rogoyski [34], and for order 11 by McKay and Wanless [35].”