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A New Expression of the q-Stirling Numbers Cai, Yue

Description

Stirling numbers of the second kind $S(n,k)$ enumerate the number of set partitions of $n$ elements into k disjoint blocks. We give a compact expression for the $q$-Stirling numbers as a $q$-$(1+q)$-analogue. We show there is a poset explanation for this phenomenon as well as a homological interpretation. This is joint work with Margaret Readdy.

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Attribution-NonCommercial-NoDerivatives 4.0 International