%0 Journal Article
%T Generalizations of Bell number formulas of Spivey and Mezo
%A Mark Shattuck
%J Mathematics
%D 2014
%I arXiv
%X We provide q-generalizations of Spivey's Bell number formula in various settings by considering statistics on different combinatorial structures. This leads to new identities involving q-Stirling numbers of both kinds and q-Lah numbers. As corollaries, we obtain identities for both binomial and q-binomial coefficients. Our results at the same time also generalize recent r-Stirling number formulas of Mezo. Finally, we provide a combinatorial proof and refinement of Xu's extension of Spivey's formula to the generalized Stirling numbers of Hsu and Shiue. To do so, we develop a combinatorial interpretation for these numbers in terms of extended Lah distributions.
%U http://arxiv.org/abs/1412.1110v1