Conference abstracts

Session B2 - Graph Theory and Combinatorics

No date set

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 Berkeley).

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