Transversals in latin squares: a survey

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Researchpeer-review

Abstract

A latin square of order n is an n x n array of n symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of n entries containing no pair of entries that share the same row, column or symbol. Transversals are closely relates to the notions of complete mappings and orthomorphisms in (quasi) groups, and are fundamental to teh concept of mutually orthogonal latin square. Here we survey the literature on transversals and related notions. We cover (1) existence and enumeration results, (2) generalisations of transversal including partial transversals and plexes, (3) the special case when the latin square is a group table, (4) a connection with covering radii of sets of permutations, (5) transversals in arrays that generalise the notion of a latin square in various ways.
Original languageEnglish
Title of host publicationSurveys in Combinatorics 2011
EditorsRobin Chapman
Place of PublicationNew York
PublisherCambridge University Press
Pages403 - 437
Number of pages35
ISBN (Print)9781107601093
Publication statusPublished - 2011

Cite this

Wanless, I. M. (2011). Transversals in latin squares: a survey. In R. Chapman (Ed.), Surveys in Combinatorics 2011 (pp. 403 - 437). Cambridge University Press.