Noncommutative Catalan numbers
Quantum Algebra
2019-10-09 v4 Combinatorics
Representation Theory
Abstract
The goal of this paper is to introduce and study noncommutative Catalan numbers which belong to the free Laurent polynomial algebra in generators. Our noncommutative numbers admit interesting (commutative and noncommutative) specializations, one of them related to Garsia-Haiman -versions, another -- to solving noncommutative quadratic equations. We also establish total positivity of the corresponding (noncommutative) Hankel matrices and introduce accompanying noncommutative binomial coefficients.
Keywords
Cite
@article{arxiv.1708.03316,
title = {Noncommutative Catalan numbers},
author = {Arkady Berenstein and Vladimir Retakh},
journal= {arXiv preprint arXiv:1708.03316},
year = {2019}
}
Comments
12 pages AM LaTex, a picture and proof of Lemma 3.6 are added, misprints corrected