We give combinatorial proofs of q-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the q-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel q-Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.
@article{10_37236_6829,
author = {Yue Cai and Richard Ehrenborg and Margaret Readdy},
title = {\(q\)-Stirling identities revisited},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/6829},
zbl = {1380.05017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6829/}
}
TY - JOUR
AU - Yue Cai
AU - Richard Ehrenborg
AU - Margaret Readdy
TI - \(q\)-Stirling identities revisited
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6829/
DO - 10.37236/6829
ID - 10_37236_6829
ER -
%0 Journal Article
%A Yue Cai
%A Richard Ehrenborg
%A Margaret Readdy
%T \(q\)-Stirling identities revisited
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6829/
%R 10.37236/6829
%F 10_37236_6829
Yue Cai; Richard Ehrenborg; Margaret Readdy. \(q\)-Stirling identities revisited. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6829
