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 containing …

Latin squares and mutually orthogonal sets of Latin squares (MOLS) have an old history
predating Euler's work in the late 1700s. With the emergence of the abstract concept of a …

An autotopism of a Latin square is a triple (α, β, γ) of permutations such that the Latin square
is mapped to itself by permuting its rows by α, columns by β, and symbols by γ. Let Atp (n) be …

A classic paper of Dickson gives a complete list of permutation polynomials of degree less
than 6 over arbitrary finite fields, and degree 6 over finite fields of odd characteristic …

A Latin square is a matrix of symbols such that each symbol occurs exactly once in each row
and column. A Latin square LL is row‐Hamiltonian if the permutation induced by each pair of …

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 …

A 1‐factorization of a graph is a decomposition of the graph into edge disjoint perfect
matchings. There is a well‐known method, which we call the 𝕂‐construction, for building a 1 …

A perfect 1-factorisation of a graph G is a decomposition of G into edge disjoint 1-factors
such that the union of any two of the factors is a Hamiltonian cycle. Let p⩾ 11 be prime. We …

We report the results of a computer enumeration that found that there are 3155 perfect 1-
factorisations (P1Fs) of the complete graph,(ii) observe that the new P1Fs produce no atomic …

The parity type of a Latin square is defined in terms of the numbers of even and odd rows
and columns. It is related to an Alon-Tarsi-like conjecture that applies to Latin squares of odd …