7 citations · 25 across the 19 of their papers we have counts for
9 papers · 1 filter
Chain decompositions of q,t-Catalan numbers: tail extensions and flagpole partitions
Seongjune Han, Kyungyong Lee, Li Li +1
This article is part of an ongoing investigation of the combinatorics of -Catalan numbers . We develop a structure theory for integer partitions based on…
Chain Decompositions of -Catalan Numbers via Local Chains
Seongjune Han, Kyungyong Lee, Li Li +1
The -Catalan number enumerates integer partitions contained in an triangle by their dinv and external area statistics. The paper [LLL18 (Lee,…
New Combinatorial Formulas for Cluster Monomials of Type A Quivers
Kyungyong Lee, Li Li, Ba Nguyen
Lots of research focuses on the combinatorics behind various bases of cluster algebras. This paper studies the natural basis of a type A cluster algebra, which consists of all clus…
A Combinatorial Approach to the Symmetry of -Catalan Numbers
Kyungyong Lee, Li Li, Nicholas A. Loehr
The \emph{-Catalan numbers} are polynomials in and that reduce to the ordinary Catalan numbers when . These polynomials have important connections to…
Positivity and tameness in rank 2 cluster algebras
Kyungyong Lee, Li Li, Andrei Zelevinsky
We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster…
Combinatorics of certain higher -Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula
Kyungyong Lee, Li Li, Nicholas A. Loehr
The higher -Catalan polynomial can be defined combinatorially as a weighted sum of lattice paths contained in certain triangles, or algebraically as a complic…