Enumeration formulas for latin and frequency squares
type: Item
instance of: scholarly article
title: Enumeration formulas for latin and frequency squares
zbMATH Open document ID: 0789.05007
DOI: 10.1016/0012-365X(93)90152-J
author: Gary L. Mullen
author: József Dénes
published in: Discrete Mathematics
publication date: 1994-01-05T00:00:00Z
review text: A frequency (quasi-latin) square is an \(n \times n\) array with entries \(1,2,\dots,m\) such that each number \(i\) occurs exactly \(\lambda_ i\) times in each row and column. Two frequency squares are isotopic if one can be obtained from the other by permuting rows, columns, and then numbers. The authors relate the number of latin squares of order \(n\) to the number of unordered 1-factorizations of reduced frequency squares from each isotopy class. Unfortunately, they note that the amount of computation needed to compute the number of latin squares of order 10 (the smallest unknown case) by these methods is still beyond the scope of currently available computers.
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 428310
zbMATH Keywords: frequency squares
zbMATH Keywords: latin squares
zbMATH Keywords: isotopy class
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
cites work: Q3720614
cites work: Q4769064
cites work: Q3786492
cites work: Q4732479
cites work: Counting Latin rectangles
cites work: Q3231172
full work available at URL: 0012-365x(93)90152-j
OpenAlex ID: W2094960002
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description: scientific article; zbMATH DE number 428310