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

Access to Document

10.1017/S0004972716000174

Cite this

@article{668e6d19ef5a46959ad0fa1b0fc6fabe,

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 → ∞.",

keywords = "Alon-Tarsi conjecture, and phrases Latin square, parity, row cycle",

author = "Cavenagh, {Nicholas J.} and Wanless, {Ian M.}",

note = "Publisher Copyright: {\textcopyright} 2016 Australian Mathematical Publishing Association Inc.",

year = "2016",

month = oct,

day = "1",

doi = "10.1017/S0004972716000174",

language = "English",

volume = "94",

pages = "187--194",

journal = "Bulletin of the Australian Mathematical Society",

issn = "0004-9727",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - There are asymptotically the same number of Latin squares of each parity

AU - Cavenagh, Nicholas J.

AU - Wanless, Ian M.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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 → ∞.

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 → ∞.

KW - Alon-Tarsi conjecture

KW - and phrases Latin square

KW - parity

KW - row cycle

UR - http://www.scopus.com/inward/record.url?scp=84979306658&partnerID=8YFLogxK

U2 - 10.1017/S0004972716000174

DO - 10.1017/S0004972716000174

M3 - Article

SN - 0004-9727

VL - 94

SP - 187

EP - 194

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this