Incomplete self-orthogonal latin squares \(ISOLS(6m+6,2m)\) exist for all m
type: Item
instance of: scholarly article
title: Incomplete self-orthogonal latin squares \(ISOLS(6m+6,2m)\) exist for all m
zbMATH Open document ID: 0723.05020
DOI: 10.1016/0012-365X(91)90137-Q
author: D. Kharzeev
published in: Discrete Mathematics
publication date: 1991-01-01T00:00:00Z
review text: A self-orthogonal latin square of order v (SOLS(v)) is a latin square of order v that is orthogonal to its transpose. An SOLS(v) is known to exist for all v except \(v=2,3,6\). It is known that an incomplete self- orthogonal latin square of order v with an empty subarray of order n (an ISOLS(v,n)), can exist only if \(v\geq 3n+1.\) Using recursive constructions the authors show that an \(ISOLS(6m+6,2m)\) exists for all m. As a consequence there exists an ISOLS(v,n) for all v and n satisfying \(v\geq 3n+1\), except for \(v=6\) and \((v,n)=(8,2)\) and perhaps excepting \((v,n)=(6m+2,2m)\), \(m\geq 2\).
reviewed by: Gary L. Mullen
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 4191650
zbMATH Keywords: self-orthogonal latin square
zbMATH Keywords: SOLS
zbMATH Keywords: incomplete self-orthogonal latin square
zbMATH Keywords: ISOLS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4191650