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arXiv · 1708.03316

Noncommutative Catalan numbers

Arkady Berenstein·Vladimir Retakh
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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.

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Arkady Berenstein, Vladimir Retakh. 2017-08-10. Noncommutative Catalan numbers. https://arxiv.org/abs/1708.03316

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