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The Dehn-Sommerville Relations and the Catalan Matroid June 30, 2017 (01:00 PM PDT - 02:30 PM PDT)
Parent Program: --
Location: MSRI: Baker Board Room
Speaker(s) Anastasia Chavez (University of California, Berkeley)
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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 d+12. Thus, to determine the f-vector of P, we only need to know approximately half of its entries. This raises the question: Which (d+12)-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.


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