Recent papers

The cyclic sieving phenomenon (with V. Reiner and D. Stanton), Journal of Combinatorial Theory A, 2004, (pdf)

Abstract The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's $q=-1$ phenomenon. The phenomenon is shown to appear in various situations, involving $q$-binomial coefficients, Polya theory, polygon dissections, non-crossing partitions, finite reflection groups, and some finite field $q$-analogues.

Mahonian Z statistics (with Jennifer Galovich), Discrete Math, to appear, (pdf)

Abstract The $Z$ statistic of Zeilberger and Bressoud is computed by summing the major index of the 2-letter subwords. We generalize this idea to other splittable Mahonian statistics. We call splittable Mahonian statistics which produce other splittable Mahonian statistics in this fashion {\it $Z$-Mahonian}. We characterize $Z$-Mahonian statistics and include several examples.

The Schur cone and the cone of log concavity, (pdf)

Abstract Let $\{h_1,h_2,\dots\}$ be a set of algebraically independent variables. We ask which vectors are extreme in the cone generated by $h_ih_j-h_{i+1}h_{j-1}$ ($i\geq j>0$) and $h_i$ ($i>0$). We call this cone the {\it cone of log concavity}. More generally, we ask which vectors are extreme in the cone generated by Schur functions of partitions with $k$ or fewer parts. We give a conjecture for which vectors are extreme in the cone of log concavity. We prove the characterization in one direction and give partial results in the other direction.

This page was last revised on July 9, 2015.

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