A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-
empty cells, and whose corresponding rows and columns contain the same sets of symbols …

A latin square of order n possessing a cyclic automorphism of order n is said to be
diagonally cyclic because its entries occur in cyclic order down each broken diagonal. More …

A $ d $-dimensional Latin hypercube of order $ n $ is a $ d $-dimensional array containing
symbols from a set of cardinality $ n $ with the property that every axis-parallel line contains …

Let G be a graph with vertex-set V= V (G) and edge-set E= E (G). A 1-factor of G (also called
perfect matching) is a factor of G of degree 1, that is, a set of pairwise disjoint edges which …

Gyárfás and Sárközy conjectured that every n× nn * n Latin square has a “cycle‐free” partial
transversal of size n− 2 n-2. We confirm this conjecture in a strong sense for almost all Latin …

Various local transformations of combinatorial structures (codes, designs, and related
structures) that leave the basic parameters unaltered are here unified under the principle of …

The sign of a Latin square is− 1 if it has an odd number of rows and columns that are odd
permutations; otherwise, it is+ 1. Let LEn and Lon be, respectively, the number of Latin …

Let L be chosen uniformly at random from among the latin squares of order n≥ 4 and let r, s
be arbitrary distinct rows of L. We study the distribution of σr, s, the permutation of the …

Paratopism is a well‐known action of the wreath product on Latin squares of order n. A
paratopism that maps a Latin square to itself is an autoparatopism of that Latin square. Let …

A Latin square has six conjugate Latin squares obtained by uniformly permuting its (row,
column, symbol) triples. We say that a Latin square has conjugate symmetry if at least two of …