<abstract xmlns="http://www.w3.org/1999/xhtml">

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

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

Department of Mathematical Sciences, School of Science

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A -analogue for the Stirling numbers of the second kind of Coxeter groups of type 

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...

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

Published Online: Jun 18, 2022

Page range: 8 - 16

Received: Mar 31, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/puma-2022-0003

Keywords
Stirling numbers of second kind, set partition, type B, restricted growth word, generating function

© 2022 Eli Bagno et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jun 18, 2022

Page range: 8 - 16

Received: Mar 31, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/puma-2022-0003

KeywordsStirling numbers of second kind, set partition, type B, restricted growth word, generating function

© 2022 Eli Bagno et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Stirling numbers of second kind, set partition, type B, restricted growth word, generating function