descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint 01 Nov 2019Embargo end date: 01 Jan 2017 English Publisher:Springer International PublishingJournal:Annals of Combinatorics, volume 23, pages 527-547 (issn: 0218-0006, eissn: 0219-3094,

Authors: Berenstein, A.; Retakh, V.;

doi: 10.1007/978-3-030-57050-7_10 , 10.1007/s00026-019-00473-4 , 10.48550/arxiv.1708.03316

arXiv: http://arxiv.org/abs/1708.03316

handle: 21.11116/0000-0006-3EFD-9 , 21.11116/0000-0006-3EFF-7 , 21.11116/0000-0006-3F00-4

Noncommutative Catalan Numbers

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Abstract

The goal of this paper is to introduce and study noncommutative Catalan numbers $C_n$ which belong to the free Laurent polynomial algebra 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 $H_m$ and introduce accompanying noncommutative binomial coefficients.

12 pages AM LaTex, a picture and proof of Lemma 3.6 are added, misprints corrected

Related Organizations

University of Oregon Eugene
United States
Rutgers, The State University of New Jersey
United States
University of Oregon
United States

Keywords

Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory

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Garsia–Haiman modules for hook partitions and Green polynomials with two variables
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