# Projections and angle sums of permutohedra

@inproceedings{Godland2020ProjectionsAA, title={Projections and angle sums of permutohedra}, author={Thomas Godland and Zakhar Kabluchko}, year={2020} }

Let (x1, . . . , xn) ∈ R. Permutohedra of types A and B are convex polytopes in R defined by P n = conv{(xσ(1), . . . , xσ(n)) : σ ∈ Sym(n)} and P n = conv{(ε1xσ(1), . . . , εnxσ(n)) : (ε1, . . . , εn) ∈ {±1} n , σ ∈ Sym(n)}, where Sym(n) denotes the group of permutations of the set {1, . . . , n}. We derive a closed formula for the number of j-faces of GP n and GP B n for a linear map G : R n → R satisfying some minor general position assumptions. In particular, we will show that the face…

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