Geodesic
Some identities involving second kind Stirling numbers of types \(B\) and \(D\)
Eli Bagno ; Riccardo Biagioli ; David Garber1
1Holon Institute of Technology
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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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 identity relates them with Eulerian numbers and the second identity interprets them as entries in a transition matrix between the elements of two standard bases of the polynomial ring $\mathbb{R}[x]$. Finally, we generalize these identities to the group of colored permutations $G_{m,n}$.
DOI : 10.37236/8703
Classification : 05A18, 05A19, 11B73, 11B68
Mots-clés : Stirling number of the second kind, Eulerian numbers, colored permutations

Eli Bagno    ; Riccardo Biagioli    ; David Garber  1

1 Holon Institute of Technology 
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     author = {Eli Bagno and Riccardo Biagioli and David Garber},
     title = {Some identities involving second kind {Stirling} numbers of types {\(B\)} and {\(D\)}},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {3},
     doi = {10.37236/8703},
     zbl = {1416.05037},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8703/}
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Eli Bagno; Riccardo Biagioli; David Garber. Some identities involving second kind Stirling numbers of types \(B\) and \(D\). The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8703

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