@inbook{af1d05b7f3264d759206fe10ecae32af,
title = "Noncommutative Catalan Numbers",
abstract = "The goal of this paper is to introduce and study noncommutative Catalan numbers Cn which belong to the free Laurent polynomial algebra Ln in n generators. Our noncommutative numbers admit interesting (commutative and noncommutative) specializations, one of them related to Garsia–Haiman (q, t)-versions, another—to solving noncommutative quadratic equations. We also establish total positivity of the corresponding (noncommutative) Hankel matrices Hn and introduce accompanying noncommutative binomial coefficients.",
keywords = "Catalan numbers, Laurent polynomials, Non-commuting variables",
author = "Arkady Berenstein and Vladimir Retakh",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",
year = "2021",
doi = "10.1007/978-3-030-57050-7_10",
language = "English (US)",
series = "Trends in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "173--193",
booktitle = "Trends in Mathematics",
address = "Germany",
}