A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B

Eli Bagno; David Garber; Takao Komatsu

doi:10.2478/puma-2022-0003

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A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B

Pure Mathematics and Applications

Volume 30 (2022): Issue 1 (June 2022)

By: Eli Bagno, David Garber and Takao Komatsu

Open Access

|Jun 2022

Abstract

A generalization of the Stirling numbers of the second kind of type B is given in two different directions. One generalization is via their q-analogue and the other one uses r distinguished elements. Both directions are explained and proved in a combinatorial way using generalized restricted growth words which we define here for type B. Moreover, we present their ordinary and exponential generating functions, where the exponential generating function is also used to present the r-variant as connection constants between two bases of ℝ[x].

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Articles in this issue

DOI: https://doi.org/10.2478/puma-2022-0003 | Journal eISSN: 1788-800X

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Language: English

Page range: 8 - 16

Submitted on: Mar 31, 2022

Accepted on: May 15, 2022

Published on: Jun 18, 2022

Published by: Corvinus University of Budapest

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Stirling numbers of second kind,

set partition,

type B,

restricted growth word,

generating function

Related subjects:

Computer sciences,

Theoretical computer sciences,

Business and economics,

Mathematics and statistics for economists,

Mathematics,

Analysis,

Differential equations and dynamical systems

© 2022 Eli Bagno, David Garber, Takao Komatsu, published by Corvinus University of Budapest
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 30 (2022): Issue 1 (June 2022)