Degree sequences of graphs have been thoroughly studied. For example, there are many characterizations for those integer sequences that are degree sequences of graphs. It is also well known which classes of graphs have distinguished properties such as maximal or unique degree sequences. Notions of generalized degree sequences for higher dimensional simplicial complexes however have not been nearly as well investigated. I will talk about work in progress on understanding these generalized degree sequences and those complexes which exhibit analogous special properties.

This talk reflects joint work with Amitava Bhattacharya, Uri Peled, and Vic Reiner.