The spectrum of \(\text{HSOLSSOM}(h^ n)\) where \(h\) is even
type: Item
instance of: scholarly article
title: The spectrum of \(\text{HSOLSSOM}(h^ n)\) where \(h\) is even
zbMATH Open document ID: 0867.05011
DOI: 10.1016/0012-365X(95)00066-6
author: Yanyan Li
published in: Discrete Mathematics
publication date: 1997-07-20T00:00:00Z
review text: An \(\text{HSOLSSOM}(h^n)\), that is, holey self-orthogonal Latin squares with a symmetric orthogonal mate, consists of three mutually orthogonal Latin squares \(A\), \(B\), and \(C\) of order \(hn\), each having \(n\) holes of size \(h\) that partition the element set, such that \(B=A^T\) and \(C=C^T\). The authors improve the known result for \(h=2\) and show that an \(\text{HSOLSSOM}(2^n)\) exists for \(n\geq 5\) except possibly for \(n\in E=\{8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 28, 32\}\). They then show that an \(\text{HSOLSSOM}(h^n)\) exists for \(n\geq 5\) except possibly for \(n\in E\) if \(h\equiv 2\text{ mod}(4)\) and \(h\geq 10\), and that it exists for \(n\geq 5\) if \(h\equiv 0\text{ mod}(4)\).
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 943215
zbMATH Keywords: holey self-orthogonal Latin squares
zbMATH Keywords: orthogonal mate
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
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full work available at URL: 0012-365x(95)00066-6
OpenAlex ID: W2150433766
description: scientific article; zbMATH DE number 943215