<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

Publié en ligne: 18 juin 2022

Pages: 8 - 16

Reçu: 31 mars 2022

Accepté: 15 mai 2022

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

Mots clés
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

Publié en ligne: 18 juin 2022

Pages: 8 - 16

Reçu: 31 mars 2022

Accepté: 15 mai 2022

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

Mots clésStirling 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.

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