Most latin squares have many subsquares

B. D. McKay, I. M. Wanless

Research output: Contribution to journalArticleResearchpeer-review

26 Citations (Scopus)

Abstract

Ak×nLatin rectangle is ak×nmatrix of entries from {1, 2, ..., n} such that no symbol occurs twice in any row or column. An intercalate is a 2×2 Latin sub-rectangle. LetN(R) be the number of intercalates inR, a randomly chosenk×nLatin rectangle. We obtain a number of results about the distribution ofN(R) including its asymptotic expectation and a bound on the probability thatN(R)=0. Forε>0 we prove most Latin squares of ordernhaveN(R)≥n3/2-ε. We also provide data from a computer enumeration of Latin rectangles for smallk, n.

Original languageEnglish
Pages (from-to)323-347
Number of pages25
JournalJournal of Combinatorial Theory. Series A
Volume86
Issue number2
DOIs
Publication statusPublished - 1 May 1999
Externally publishedYes

Cite this