2015/12/14 by Chavez, Anastasia, Yamzon, Nicole
#52B05 #52B40 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1512.04513
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 bases of the Catalan matroid.