Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Transversals in latin squares
Authors: I. M. Wanless
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Abstract
A latin square of order n is an n×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.Fulltext
– 0.30 Mb
Contents
- Advances in loop rings and their loops
- Central automorphisms of Latin square designs and loops
- Loops related to geometric structures
- Computing with small quasigroups and loops
- Connected transversals and multiplication groups of loops
- Four lectures on quasigroup representations
- Gyrogroups, the grouplike loops in the service of hyperbolic geometry and Einstein's special theory of relativity
- Transversals in latin squares
