Colloquium / Seminars

Topic：The Colored Generalizations of Stirling numbers of both kinds and the Lah numbers
Speaker：Prof. Louis Kao
　　　　(Dept. of Mathematics, Fu-Jen University)
Date time：April 22, 2025 (Tue) 14:00 –15:00
Venue：SA213
Abstract：
Abstract. Recently in the area of enumerative combinatorics, the $q$-analogue of combinatorial structures have been studied widely. Specifically, the aim of this work is to identify two statistics over combinatorial structure $S$ and a proper subset $S'$ of $S$ such that the$q$-analogue represents the $q$-$(1+q)$-expansion over $S'$, and to explore the poset and topological interpretations of this expansion. People provided comprehensive profiles for several integer sequences like classical Stirling numbers of both kinds and Catalan number within this framework. In this work, we extend the work on 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 $D$.

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