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Dehn-Sommerville relations and the Catalan Matroid

Algebra & Discrete Mathematics

Speaker: Anastasia Chavez, UCB
Location: 1147 MSB
Start time: Mon, Feb 22 2016, 1:10PM

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 $\lceil{\frac{d+1}{2}}\rceil$. Thus, to determine the $f$-vector of $P$, we only need to know approximately half of its entries. This raises the question: Which $(\lceil{\frac{d+1}{2}}\rceil)$-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. This is joint work with Nicole Yamzon.