Most latin squares have many subsquares

B. D. McKay*, I. M. Wanless

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    35 Citations (Scopus)


    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
    Issue number2
    Publication statusPublished - May 1999


    Dive into the research topics of 'Most latin squares have many subsquares'. Together they form a unique fingerprint.

    Cite this