Mathematics Colloquia and Seminars

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Description

Face enumeration of simplicial complexes is a central topic in geometric combinatorics, and partitionability is a key combinatorial tool to study the associated f-vector. For objects like polytopes and regular CW spheres, one may wish to not only count the number of faces of each dimension but also keep track of all chains of faces. The flag f-vector will record all possible chains of faces. In its most concise form, the flag f-vector is expressed via the cd-index, defined by Fine and Bayer-Klapper. In this talk, I will discuss how the concept of partitionability can be extended to study the cd-index. Namely, I will define the class of S-partitionable posets, demonstrate how they generalize (Eulerian) partitionable simplicial complexes, and illustrate how they admit a recursive combinatorial decomposition that allows one to compute a nonnegative cd-index. This is based on recent joint work with Felipe Caster and José Samper.