Abstracts
for the Seminar

Spring 2016

**Speaker: **Anastasia Chavez, University of California, Berkeley

**Title: **The Dehn-Sommerville relations and the Catalan matroid

**Time:** 2:30 PM, Monday, April 25, 2016

**Place:** Malott 206

**Abstract:** The $f$-vector of a $d$-dimensional polytope $P$ stores the number of faces of each dimension. When $P$ is simplicial the Dehn-Sommerville relations condense the $f$-vector into the g-vector, which has length $\lceil{(d+1)/2}\rceil$. Thus, to determine the $f$-vector of $P$, we only need to know approximately half of its entries. This raises the question: Which $\lceil{(d+1)/2}\rceil$ subsets of the $f$-vector of a general simplicial polytope are sufficient to determine the whole $f$-vector? We prove that the answer is given by the Catalan matroid. This is joint work with Nicole Yamzon.

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