Conference abstracts

Session S06 - Algebraic Combinatorics

July 25, 18:00 ~ 18:25

## The Dehn--Sommerville Relations and the Catalan matroid

### Nicole Yamzon

### San Francisco State University, United States - nyamzon@mail.sfsu.edu

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 imply that to determine the $f$-vector of $P$, we only need to know approximately half of its entries. This raises the question: Which $(\lceil{\frac{d+1}{2}}\rceil)$-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 bases of the Catalan matroid.

Joint work with Anastasia Chavez (University of California at Berkeley).