How many \(7\times 7\) latin squares can be partitioned into Youden squares?
type: Item
instance of: scholarly article
title: How many \(7\times 7\) latin squares can be partitioned into Youden squares?
zbMATH Open document ID: 0835.05008
DOI: 10.1016/0012-365X(94)00216-6
author: D. A. Preece
published in: Discrete Mathematics
publication date: 1996-02-15T00:00:00Z
review text: A \(k \times v\) Youden square is a \(k \times v\) array where the set of symbols in the columns of the rectangle are the \(v\) blocks in a symmetric \((v,k, \lambda)\) balanced incomplete block design and in addition the array is row latin. This paper enumerates the number of \(7 \times 7\) latin squares that can be partitioned into a \(3 \times 7\) and a \(4 \times 7\) Youden square. The main results of this paper are that of the 564 isotopy classes of \(7 \times 7\) latin squares, 29 consist of squares that can be partitioned into \(3 \times 7\) and \(4 \times 7\) Youden squares; these 29 isotopy classes belong to 19 of the 147 main classes of \(7 \times 7\) latin squares.
reviewed by: J. H. Dinitz
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 744025
zbMATH Keywords: Youden square
zbMATH Keywords: array
zbMATH Keywords: balanced incomplete block design
zbMATH Keywords: latin squares
zbMATH Keywords: isotopy classes
MaRDI profile type: Publication
cites work: THE 7 × 7 SQUARES
cites work: Q4388205
cites work: ORTHOGONAL LATIN SQUARES
cites work: Q3476817
cites work: An Omission in Norton's List of $7 \times 7$ Squares
description: scientific article; zbMATH DE number 744025