Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775444 | Advances in Applied Mathematics | 2017 | 31 Pages |
Abstract
We show the classical q-Stirling numbers of the second kind can be expressed compactly as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in q and 1+q. We extend this enumerative result via a decomposition of a new poset Î (n,k) which we call the Stirling poset of the second kind. Its rank generating function is the q-Stirling number Sq[n,k]. The Stirling poset of the second kind supports an algebraic complex and a basis for integer homology is determined. A parallel enumerative, poset theoretic and homological study for the q-Stirling numbers of the first kind is done. Letting t=1+q we give a bijective argument showing the (q,t)-Stirling numbers of the first and second kinds are orthogonal.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yue Cai, Margaret A. Readdy,