University of Washington

One way to define an integer polymatroid ρ is via its independent set polytope, whose faces are parallel translations of the independent set polytopes of the minors of ρ. To better understand the interior of this polytope, we endow a structure on...

In this talk, we consider colored permutation groups ℤm≀Sn, which contain the symmetric groups Sn≅ℤ1≀Sn and the signed symmetric groups Bn≅ℤ2≀Sn as special cases. Like in Sn, colored permutations in ℤm≀Sn have a notion of cycle type that classifies...

A d-polytope is called (d−i)-simplicial if all of its (d−i)-faces are simplices. It is i-simple if every (d−i−1)-face belongs to exactly i+1 facets. A few low-dimensional examples of (d−i)-simplicial i-simple polytopes arising from regular polytopes...

We study the behavior of h-vectors associated to matroid complexes under weak maps, or inclusions of matroid polytopes. Specifically, we show that the h-vector of the order complex of the lattice of flats of a matroid is component-wise non-increasing...

We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner...

The inhomogeneous multispecies PushTASEP is an interacting particle system with multiple species of particles on a finite ring where the hopping rates are site-dependent. (The homogeneous variant on Z is also known as the Hammersley–Aldous–Diaconis...

Tadao Oda conjectured that every smooth polytope, in any dimension, has the Integer Decomposition Property. Beck et al. previously showed that smooth polytopes which are both 3-dimensional and centrally symmetric have this property. We show this...

In characteristic zero, the Hopf algebra of quasisymmetric functions QSym is isomorphic to the shuffle algebra of compositions Sh, and isomorphisms between them can be specified via shuffle bases of QSym. We give characterizations of shuffle bases...

The Schensted correspondence is a bijection between permutations in Sn and pairs of standard Young tableaux (P,Q) with n boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated...

A harmonic function of one variable is a linear function. A harmonic function of two variables is the real or imaginary part of an analytic function. A harmonic function of n variables is a function u satisfying \frac{\partial^{2}u}{\partial x_{1}^{2...