This paper discusses critical sets for latin squares. We give the cardinality of the minimal critical set for a family of latin squares and for latin squares of small order. Disciplines Physicalâ€¦ (More)

A Î¼-way Latin trade of volume s is a collection of Î¼ partial Latin squares T1, T2, . . . , TÎ¼, containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a differentâ€¦ (More)

Traditional knowledge, promoted to make conservation and development more relevant and socially acceptable, is shown to have an important role in identifying critical research needs in tropicalâ€¦ (More)

This paper provides constructions that prove that critical sets exist of all sizes between L ~2 J and n2;n, with the exception of rf + 1 for even n, in a latin square of order n.

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into sixâ€¦ (More)

In 1998 Donovan and Howse proved that for all n there exist critical sets of order n and size s, where l rt J ~ s ~ n2;n with the exception of the case s = rt + 1 when n is even. In this paper weâ€¦ (More)

In recent times there has been some interest in studying partial latin squares which have no completions or precisely one completion, and which are critical with respect to this property. Suchâ€¦ (More)

In this talk I will review the concept of the biembedding of two latin squares. Of particular interest will be the regular biemedding of two isomorphic copies of the latin square corresponding to theâ€¦ (More)