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.

引用

页码：796 / 807

页数：12

共 13 条

[1] Indivisible plexes in latin squares [J].

Bryant, Darryn ;

Egan, Judith ;

Maenhaut, Barbara ;

Wanless, Ian M. .

DESIGNS CODES AND CRYPTOGRAPHY, 2009, 52 (01) :93-105

[2]

Denes J., 1974, LATIN SQUARES THEIR

[3] Maximal sets of mutually orthogonal Latin squares [J].

Drake, DA ;

van Rees, GHJ ;

Wallis, WD .

DISCRETE MATHEMATICS, 1999, 194 (1-3) :87-94

[4] MAXIMAL SETS OF LATIN SQUARES AND PARTIAL TRANSVERSALS [J].

DRAKE, DA .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1977, 1 (02) :143-149

[5]

EGAN J, LATIN SQUARES UNPUB

[6]

EGAN J, J COMBIN DE IN PRESS

[7] Latin Squares with No Small Odd Plexes [J].

Egan, Judith ;

Wanless, Ian M. .

JOURNAL OF COMBINATORIAL DESIGNS, 2008, 16 (06) :477-492

[8] Indivisible partitions of latin squares [J].

Egan, Judith ;

Wanless, Ian M. .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2011, 141 (01) :402-417

[9] Latin squares without orthogonal mates [J].

Evans, AB .

DESIGNS CODES AND CRYPTOGRAPHY, 2006, 40 (01) :121-130

[10] Atomic Latin squares of order eleven [J].

Maenhaut, BM ;

Wanless, IM .

JOURNAL OF COMBINATORIAL DESIGNS, 2004, 12 (01) :12-34

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