Abstract H. G. Landau has characterized those integer-sequences S = (s1, s2, . . . , sn) which can arise as score-vectors in an ordinary round-robin tournament among n contestants [17]. If s1 ≤ s2 ≤… Expand

Abstract Necessary and sufficient conditions are given for a doubly stochastic matrix D to be expressible as a convex combination of permutation matrices distinct from the identity, thus solving a… Expand

Abstract The elements in the group of centrosymmetric n × n permutation matrices are the extreme points of a convex subset of n 2 -dimensional Euclidean space, which we characterize by a very simple… Expand

Each extreme point in the convex set @D^*"n of all nxn symmetric doubly-stochastic matrices is shown to have the form 12(P + P^t), for some nx n permutation matrix P.Expand

In 1960 Trevor Evans proved that a finite partial quasigroup of order n could be embedded in a finite quasigroup of order In [4]. Evans' Theorem on the finite embeddability of partial quasigroups was… Expand

Abstract A method is described for obtaining the facets of certain convex polyhedra from the optimal solutions to a related linear programming problem. This approach provides a direct proof, via the… Expand