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.

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