The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

The class of tournaments is by far the most well-studied class of digraphs with many deep
and important results. Since Moon's pioneering book in 1968 [146], the study of tournaments …

Two new elementary proofs are given of Landau's Theorem on necessary and sufficient
conditions for a sequence of integers to be the score sequence for some tournament. The …

In line with the trend of Coxeter combinatorics, and in response to a question of Stanley, we
show that the Coxeter permutahedra, recently studied by Ardila, Castillo, Eur and Postnikov …

Using Rado's theorem for the existence of an independent transversal of family of subsets of
a set on which a matroid is defined, we give a proof of Landau's theorem for the existence of …

Let $ a,\b\(b\geq a) $ and $ n\(n\geq 2) $ be nonnegative integers and let $\mathcal {T}(a, b,
n) $ be the set of such generalised tournaments, in which every pair of distinct players is …

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops.
The score of a vertex vi in an oriented graph D is a_ v_i (or simply ai) d_ v_i^-are the …

A tournament of order n is usually considered as an orientation of the complete graph K n. In
this note, we consider a more general definition of a tournament that we call a C-tournament …

We extend the Bruhat order on the set S n of permutations (permutation matrices) of {1, 2,…,
n} and its generalization to classes A (R, S) of (0, 1)-matrices with row sum vector R and …