On the Number of Latin Squares
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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 1/2n, (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...[Show more]
dc.contributor.author | McKay, Brendan | |
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dc.contributor.author | Wanless, Ian | |
dc.date.accessioned | 2015-12-13T22:59:09Z | |
dc.identifier.issn | 0218-0006 | |
dc.identifier.uri | http://hdl.handle.net/1885/83637 | |
dc.description.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 1/2n, (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. | |
dc.publisher | Birkhauser Verlag | |
dc.source | Annals of Combinatorics | |
dc.subject | Keywords: 1-factorisation; Enumeration; Latin square; Permanent; Regular bipartite graph | |
dc.title | On the Number of Latin Squares | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
local.identifier.citationvolume | 9 | |
dc.date.issued | 2005 | |
local.identifier.absfor | 010104 - Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | |
local.identifier.ariespublication | MigratedxPub11920 | |
local.type.status | Published Version | |
local.contributor.affiliation | McKay, Brendan, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Wanless, Ian, College of Engineering and Computer Science, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 335 | |
local.bibliographicCitation.lastpage | 344 | |
local.identifier.doi | 10.1007/s00026-005-0261-7 | |
dc.date.updated | 2015-12-12T07:26:51Z | |
local.identifier.scopusID | 2-s2.0-26044433646 | |
Collections | ANU Research Publications |
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