Drew Armstrong

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20172025

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math.CO2025

Cyclic Sieving of Multisets with Bounded Multiplicity and the Frobenius Coin Problem

Drew Armstrong

The two subjects in the title are related via the specialization of symmetric polynomials at roots of unity. Let $f (z_{1}, \dots, z_{n}) \in Z [z_{1}, \dots, z_{n}]$ be a symmetric pol…

math.CO2024

Lattice Points and Rational $q$ -Catalan Numbers

Drew Armstrong

For each pair of coprime integers $a$ and $b$ we have a rational $q$ -Catalan number $Cat (a, b)_{q} = (a a + b)_{q} / [a + b]_{q}$ . It is known that this is a polynomial in $…

math.CO2017

The Waldspurger Transform of Permutations and Alternating Sign Matrices

James McKeown

In 2005 J.L. Waldspurger proved the following theorem: given a finite real reflection group $W$ , the closed positive root cone is tiled by the images of the open weight cone under…

Cyclic Sieving of Multisets with Bounded Multiplicity and the Frobenius Coin Problem

Lattice Points and Rational q-Catalan Numbers

The Waldspurger Transform of Permutations and Alternating Sign Matrices

Lattice Points and Rational $q$ -Catalan Numbers