T. Kyle Petersen

Learn More
The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions ((Kas61), (TF61)). In earlier work, Stanley (Sta85) proved a reciprocity principle governing the number N(m, n) of dimer coverings of an m by n rectangular(More)
We show that the set R(w 0) of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. More specifically, R(w 0) possesses a natural cyclic action given by moving the first letter of a word to the end, and we show that the orbit structure of this action is encoded by the generating function for the(More)
We present examples of flag homology spheres whose γ-vectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit simplicial complexes whose f-vectors are(More)
For a polynomial with palindromic coefficients, unimodality is equivalent to having a nonnegative g-vector. A sufficient condition for unimodality is having a non-negative γ-vector, though one can have negative entries in the γ-vector and still have a nonnegative g-vector. In this paper we provide combinatorial models for three families of γ-vectors that(More)