Coxeter-biCatalan combinatorics
Abstract
We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count "twin" pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics.
Keywords
Cite
@article{arxiv.1605.03524,
title = {Coxeter-biCatalan combinatorics},
author = {Emily Barnard and Nathan Reading},
journal= {arXiv preprint arXiv:1605.03524},
year = {2026}
}
Comments
53 pages, 8 figures. version2: Small expository changes to reflect the fact that "double-positive" Catalan polynomials have already appeared as the local h-polynomials of the positive cluster complex (Athanasiadis-Savvidou). version3: Expository changes reflecting referee suggestions. To appear in JACo