A Latin square is pan-Hamiltonian if every pair of rows forms a single cycle. Such squares are related to perfect 1-factorisations of the complete bipartite graph. A square is atomic if everyâ€¦ (More)

We study the covering radius of sets of permutations with respect to the Hamming distance. Let f(n, s) be the smallest number m for which there is a set of m permutations in Sn with covering radius râ€¦ (More)

We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, (2) answer some questions of Alter by showing that theâ€¦ (More)

It is well known that if n is even, the addition table for the integersmodulo n (whichwe denote by Bn) possesses no transversals.We show that ifn is odd, then the number of transversals in Bn is atâ€¦ (More)

For a finite triangulation of the plane with faces properly coloured white and black, let AW be the abelian group constructed by labelling the vertices with commuting indeterminates and addingâ€¦ (More)

Let n denote the set of (0; 1)-matrices of order n with exactly k ones in each row and column. Let Ji be such that i = {Ji} and for Aâˆˆ n de ne Aâˆˆ nâˆ’k n by A = Jn âˆ’ A. We are interested in theâ€¦ (More)

A Latin square of order n is an n Ã— n array of n symbols, in which each symbol occurs exactly once in each row and column. A transversal is a set of n entries, one selected from each row and eachâ€¦ (More)

Let L be chosen uniformly at random from among the latin squares of order n â‰¥ 4 and let r, s be arbitrary distinct rows of L. We study the distribution of Ïƒr,s, the permutation of the symbols of Lâ€¦ (More)

The sign of a Latin square is âˆ’1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. Let Ln and L o n be, respectively, the number of Latin squares of order nâ€¦ (More)