Monogamous latin squares

被引：12
|
作者：
Danziger, Peter [1 ]
Wanless, Ian M. [2 ]
Webb, Bridget S. [3 ]
机构：
[1] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada
[2] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia
[3] Open Univ, Milton Keynes MK7 6AA, Bucks, England
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2011年 / 118卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Latin square; Monogamous square; MOLS; maxMOLS; Transversal; ORTHOGONAL MATES; MAXIMAL SETS; TRANSVERSALS; PLEXES;
D O I：
10.1016/j.jcta.2010.11.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show for all n is not an element of {1, 2, 4} that there exists a latin square of order n that contains two entries gamma(1) and gamma(2) such that there are some transversals through gamma(1) but they all include gamma(2) as well. We use this result to show that if n > 6 and n is not of the form 2p for a prime p >= 11 then there exists a latin square of order n that possesses an orthogonal mate but is not in any triple of MOLS. Such examples provide pairs of 2-maxMOLS. (C) 2010 Elsevier Inc. All rights reserved.
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页码：796 / 807
页数：12
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