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

A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B AbstractA 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]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure Mathematics and Applications de Gruyter

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

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Publisher
de Gruyter
Copyright
© 2022 Eli Bagno et al., published by Sciendo
eISSN
1788-800X
DOI
10.2478/puma-2022-0003
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Abstract

AbstractA 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].

Journal

Pure Mathematics and Applications – de Gruyter

Published: Jun 1, 2022

Keywords: Stirling numbers of second kind; set partition; type B; restricted growth word; generating function; 05A18; 05A30; 11B73

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