TY - JOUR
T1 - Colored q-Stirling and q-Lah numbers
T2 - A new view continued
AU - Eu, Sen Peng
AU - Kao, Louis
AU - Lin, Juei Yin
N1 - Publisher Copyright:
© 2025 Elsevier Inc.
PY - 2025/7
Y1 - 2025/7
N2 - Cai and Readdy proposed a new framework for studying the q-analogue f(q) of a combinatorial structure S. Specifically, the aim is to identify two statistics over S and a proper subset S′ of S such that f(q) represents the q-(1+q)-expansion over S′, and to explore the poset and topological interpretations of this expansion. Cai and Readdy provided comprehensive profiles for classical Stirling numbers of both kinds within this framework. In this work, we extend Cai and Readdy's results to colored q-Stirling numbers of both kinds, as well as colored q-Lah numbers. We also briefly discuss q-Stirling and q-Lah numbers of type D.
AB - Cai and Readdy proposed a new framework for studying the q-analogue f(q) of a combinatorial structure S. Specifically, the aim is to identify two statistics over S and a proper subset S′ of S such that f(q) represents the q-(1+q)-expansion over S′, and to explore the poset and topological interpretations of this expansion. Cai and Readdy provided comprehensive profiles for classical Stirling numbers of both kinds within this framework. In this work, we extend Cai and Readdy's results to colored q-Stirling numbers of both kinds, as well as colored q-Lah numbers. We also briefly discuss q-Stirling and q-Lah numbers of type D.
KW - Lah numbers
KW - Partially-ordered set
KW - Stirling numbers
KW - Topological interpretations
KW - q-Analog
KW - r-Colored combinatorial structures
UR - https://www.scopus.com/pages/publications/105002149067
UR - https://www.scopus.com/pages/publications/105002149067#tab=citedBy
U2 - 10.1016/j.aam.2025.102889
DO - 10.1016/j.aam.2025.102889
M3 - Article
AN - SCOPUS:105002149067
SN - 0196-8858
VL - 168
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
M1 - 102889
ER -