In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that… (More)

Let U5 be the tournament with vertices v1, . . . , v5 such that v2 → v1, and vi → v j if j − i ≡ 1, 2 (mod 5) and {i, j} = {1,2}. In this article, we describe the tournaments that do not have U5 as a… (More)

BACKGROUND
Hypertension treatment guidelines recommend that blood pressure (BP) be lowered to <140/90 mm Hg, but that a reduction to <130/80 mm Hg be adopted in patients at high cardiovascular (CV)… (More)

We consider the homogeneous components Ur of the map on R = k[x, y, z]/(xA, yB , zC) that multiplies by x + y + z. We prove a relationship between the Smith normal forms of submatrices of an… (More)

Let Q(n, c) denote the minimum clique number over graphs with n vertices and chromatic number c. We investigate the asymptotics of Q(n, c) when n/c is held constant. We show that when n/c is an… (More)

In this paper we consider mixed volumes of combinations of hypersimplices. These numbers, called “mixed Eulerian numbers”, were first considered by A. Postnikov and were shown to satisfy many… (More)

In this paper we look at the crossing number, pair crossing number, and odd crossing number of graphs on a disk with multiple holes. We provide an upper bound ⌊ (n−1)2 4 ⌋ for the odd crossing number… (More)

The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a… (More)