Abstract
Using Reiner’s definition of Stirling numbers of the second kind in types B and D, we generalize two well known identities concerning the classical Stirling numbers of the second kind. The first relates them with Eulerian numbers and the second uses them as entries in a transition matrix between the elements of two standard bases of the polynomial ring in one variable.
| Original language | English |
|---|---|
| Article number | #38 |
| Journal | Seminaire Lotharingien de Combinatoire |
| Issue number | 82 |
| State | Published - 2019 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019, Seminaire Lotharingien de Combinatoire. All Rights Reserved.
Funding
§[email protected] ¶[email protected] ‖[email protected] This research was supported by a grant from the Ministry of Science and Technology, Israel, and the France’s Centre National pour la Recherche Scientifique (CNRS).
| Funders | Funder number |
|---|---|
| France’s Centre National pour la Recherche Scientifique | |
| Centre National de la Recherche Scientifique | |
| Ministry of science and technology, Israel |
Keywords
- Coxeter groups
- Eulerian numbers
- Stirling numbers of the second kind
- descent number
- falling factorial
- hyperplane arrangements
- permutation statistics