Transversals in Latin Squares

Details Transversals in Latin Squares Transversals in Latin Squares

2009-03-30

arxiv.org/abs/0903.5142v1

Quasigroups Related Systems 15, (2007) 169-190

Mathematics

Combinatorics

22 page survey article

Scientific paper

A latin square of order $n$ is an $n\times n$ 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 such that no two entries share the same row, column or symbol. Transversals are closely related to the notions of complete mappings and orthomorphisms in (quasi)groups, and are fundamental to the concept of mutually orthogonal latin squares. Here we provide a brief survey of the literature on transversals. We cover (1) existence and enumeration results, (2) generalisations of transversals 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. The survey includes a number of conjectures and open problems.

Affiliated with

Also associated with

No associations

Rating

Transversals in Latin Squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transversals in Latin Squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transversals in Latin Squares will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-424548