In this paper, we consider the q-analogue of the Hankel determinants of the Bell numbers and give combinatorial proofs of these results. We show that the Hankel determinants of the q-Stirling numbers can be simplified to a determinant that is almost upper-triangular, and then construct sign-reversing involutions on certain sets of RG-words that give rise to the determinants.
@article{10_37236_12713,
author = {Yue Cai and Ting Yang},
title = {Hankel determinants of {\(q\)-Stirling} numbers},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {3},
doi = {10.37236/12713},
zbl = {1548.05042},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12713/}
}
TY - JOUR
AU - Yue Cai
AU - Ting Yang
TI - Hankel determinants of \(q\)-Stirling numbers
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12713/
DO - 10.37236/12713
ID - 10_37236_12713
ER -
%0 Journal Article
%A Yue Cai
%A Ting Yang
%T Hankel determinants of \(q\)-Stirling numbers
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12713/
%R 10.37236/12713
%F 10_37236_12713
Yue Cai; Ting Yang. Hankel determinants of \(q\)-Stirling numbers. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12713
