4 papers · 1 filter
Universal Hilbert series coefficients of the superspace coinvariant ring
Sylvie Corteel, John Lentfer
The coefficients that determine the Hilbert series of the superspace coinvariant ring are indexed by hook-shaped partitions. We give a manifestly positive combinatorial interpretat…
Lecture hall graphs and the Askey scheme
Sylvie Corteel, Bhargavi Jonnadula, Jonathan P. Keating +1
We establish, for every family of orthogonal polynomials in the -Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths…
Colored vertex models and -tilings of the Aztec diamond
Sylvie Corteel, Andrew Gitlin, David Keating
We study -tilings (-tuples of domino tilings) of the Aztec diamond of rank . We assign a weight to each -tiling, depending on the number of dominos of certain types and…
Rhombic staircase tableaux and Koornwinder polynomials
Sylvie Corteel, Olya Mandelshtam, Lauren Williams
In this article we give a combinatorial formula for a certain class of Koornwinder polynomials, also known as Macdonald polynomials of type . In particular, we give a co…