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THERE ARE ASYMPTOTICALLY THE SAME NUMBER OF LATIN SQUARES OF EACH PARITY

Part of: Designs and configurations

Published online by Cambridge University Press:  21 July 2016

NICHOLAS J. CAVENAGH  and
IAN M. WANLESS
NICHOLAS J. CAVENAGH
Affiliation:
Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand email nickc@waikato.ac.nz
IAN M. WANLESS*
Affiliation:
School of Mathematical Sciences, Monash University, Victoria 3800, Australia email ian.wanless@monash.edu
*
✉ian.wanless@monash.edu
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Abstract

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A Latin square is reduced if its first row and first column are in natural order. For Latin squares of a particular order $n$, there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality between the numbers of reduced Latin squares of each possible parity as the order $n\rightarrow \infty$.

Keywords

Latin squareparityAlon–Tarsi conjecturerow cycle

MSC classification

Primary: 05B15: Orthogonal arrays, Latin squares, Room squares
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 2 , October 2016 , pp. 187 - 194
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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