There are asymptotically the same number of Latin squares of each parity

Nicholas J. Cavenagh; Ian M. Wanless

doi:10.1017/S0004972716000174

There are asymptotically the same number of Latin squares of each parity

Nicholas J. Cavenagh, Ian M. Wanless^*

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

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 → ∞.

Original language	English
Pages (from-to)	187-194
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	94
Issue number	2
DOIs	https://doi.org/10.1017/S0004972716000174
Publication status	Published - 1 Oct 2016
Externally published	Yes

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title = "There are asymptotically the same number of Latin squares of each parity",

abstract = "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 → ∞.",

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AB - 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 → ∞.

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DO - 10.1017/S0004972716000174

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There are asymptotically the same number of Latin squares of each parity

Abstract

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