2 citations · 2 across the 2 of their papers we have counts for
3 papers
math.MG2016
Small f-vectors of 3-spheres and of 4-polytopes
Philip Brinkmann, Günter M. Ziegler
We present a new algorithmic approach that can be used to determine whether a given quadruple is the f-vector of any convex 4-dimensional polytope. By implement…
math.CO2016
Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
Karim Adiprasito, Philip Brinkmann, Arnau Padrol +3
The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained…
math.MG2015★ 2 cited
A flag vector of a 3-sphere that is not the flag vector of a 4-polytope
Philip Brinkmann, Günter M. Ziegler
We present a first example of a flag vector of a polyhedral sphere that is not the flag vector of any polytope. Namely, there is a unique 3-sphere with the parameters $(f_0,f_1,f_2…