Subsquares in orthogonal Latin squares as subspaces in affine geometries: A generalization of an equivalence of Bose
type: Item
instance of: scholarly article
title: Subsquares in orthogonal Latin squares as subspaces in affine geometries: A generalization of an equivalence of Bose
zbMATH Open document ID: 0772.05017
DOI: 10.1007/BF01389352
author: Charles F. Laywine
published in: Designs, Codes and Cryptography
publication date: 1993-05-16T00:00:00Z
review text: From author's abstract: The combinatorial properties of subsquares in orthogonal Latin squares are examined. Using these properties it is shown that in appropriate orthogonal Latin squares of order \(m^ h\) blocks of subsquares of order \(m^{h(i-1)/i}\), where \(i\) divides \(h\), form the hyperplanes of the affine geometry \(\text{AG}(2i,m^{h/i})\). This means that a given set of mutually orthogonal Latin squares may be equivalent simultaneously to a number of different geometries depending on the order of the subsquares used to form the hyperplanes. In the case that \(i=1\), the subsquares become points, the hyperplanes become lines, and the equivalence reduces to the well-known result of Bose relating orthogonal Latin squares and affine planes.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E05
zbMATH DE Number: 167547
zbMATH Keywords: equivalence of Bose
zbMATH Keywords: orthogonal Latin squares
zbMATH Keywords: hyperplanes
zbMATH Keywords: affine geometry
reviewed by: Katherine Heinrich
MaRDI profile type: Publication
cites work: Q3990640
cites work: Q5598099
cites work: Q4282949
cites work: Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes
cites work: Q3680841
cites work: On the structure of affine designs
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description: scientific article; zbMATH DE number 167547