2010/06/30 by Agnarsson, Geir · 1 citation
#05A15 #05A16 #52B05 #52B11 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1006.5928
For a polytope we define the \em flag polynomial, a polynomial in commuting variables related to the well-known flag vector and describe how to express the the flag polynomial of the Minkowski sum of k standard simplices in a direct and canonical way in terms of the \em k-th master polytope P(k) where k∈\nats. The flag polynomial facilitates many direct computations. To demonstrate this we provide two examples; we first derive a formula for the f-polynomial and the maximum number of d-dimensional faces of the Minkowski sum of two simplices. We then compute the maximum discrepancy between the number of (0,d)-chains of faces of a Minkowski sum of two simplices and the number of such chains of faces of a simple polytope of the same dimension and on the same number of vertices.