Monogamous latin squares

Peter Danziger; Ian M. Wanless; Bridget S. Webb

doi:10.1016/j.jcta.2010.11.011

Monogamous latin squares

Peter Danziger^*, Ian M. Wanless, Bridget S. Webb

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We show for all nγ{1,2,4} that there exists a latin square of order n that contains two entries γ1 and γ2 such that there are some transversals through γ1 but they all include γ2 as well. We use this result to show that if n>6 and n is not of the form 2. p for a prime pγ11 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.

Original language	English
Pages (from-to)	796-807
Number of pages	12
Journal	Journal of Combinatorial Theory. Series A
Volume	118
Issue number	3
DOIs	https://doi.org/10.1016/j.jcta.2010.11.011
Publication status	Published - Apr 2011
Externally published	Yes

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10.1016/j.jcta.2010.11.011

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title = "Monogamous latin squares",

abstract = "We show for all nγ{1,2,4} that there exists a latin square of order n that contains two entries γ1 and γ2 such that there are some transversals through γ1 but they all include γ2 as well. We use this result to show that if n>6 and n is not of the form 2. p for a prime pγ11 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.",

keywords = "Latin square, MOLS, MaxMOLS, Monogamous square, Transversal",

author = "Peter Danziger and Wanless, {Ian M.} and Webb, {Bridget S.}",

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language = "English",

volume = "118",

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T1 - Monogamous latin squares

AU - Danziger, Peter

AU - Wanless, Ian M.

AU - Webb, Bridget S.

PY - 2011/4

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N2 - We show for all nγ{1,2,4} that there exists a latin square of order n that contains two entries γ1 and γ2 such that there are some transversals through γ1 but they all include γ2 as well. We use this result to show that if n>6 and n is not of the form 2. p for a prime pγ11 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.

AB - We show for all nγ{1,2,4} that there exists a latin square of order n that contains two entries γ1 and γ2 such that there are some transversals through γ1 but they all include γ2 as well. We use this result to show that if n>6 and n is not of the form 2. p for a prime pγ11 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.

KW - Latin square

KW - MOLS

KW - MaxMOLS

KW - Monogamous square

KW - Transversal

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U2 - 10.1016/j.jcta.2010.11.011

DO - 10.1016/j.jcta.2010.11.011

M3 - Article

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VL - 118

SP - 796

EP - 807

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 3

ER -

Monogamous latin squares

Abstract

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