Abstract:

The notion of Rees product of posets was introduced by Anders Björner and Volkmar Welker as part of a study dealing with connections between poset topology and commutative algebra. By computing the homology of certain Rees product posets, John Shareshian and I discovered some surprising enumerative results. These include a q-analog of a formula of Euler for the exponential generating function of the Eulerian polynomials. Our q-analog involves the joint distribution of major index and excedance number. In this talk I will discuss the particular Rees product posets that led to our enumerative results and present some open problems on the homology of these and other Rees product posets.