The recent interest in type B $q$-Stirling numbers of the second kind prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which turns out to be a $q$-analogue of an identity due to Bagno, Biagioli and Garber. We provide a combinatorial proof of this identity and an algebraic proof of a more general identity for colored permutations. In addition, we prove some $q$-identities about the $q$-Stirling numbers of the second kind in types A, B and D.
@article{10_37236_12147,
author = {Mingjian Ding and Jiang Zeng},
title = {Some identities involving {\(q\)-Stirling} numbers of the second kind in type {B}},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/12147},
zbl = {1533.05027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12147/}
}
TY - JOUR
AU - Mingjian Ding
AU - Jiang Zeng
TI - Some identities involving \(q\)-Stirling numbers of the second kind in type B
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/12147/
DO - 10.37236/12147
ID - 10_37236_12147
ER -
%0 Journal Article
%A Mingjian Ding
%A Jiang Zeng
%T Some identities involving \(q\)-Stirling numbers of the second kind in type B
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/12147/
%R 10.37236/12147
%F 10_37236_12147
Mingjian Ding; Jiang Zeng. Some identities involving \(q\)-Stirling numbers of the second kind in type B. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12147
