Resumen de The harmonic polytope

Federico Ardila, Laura Escobar

• We study the harmonic polytope, which arose in Ardila, Denham, and Huh’s work on the Lagrangian geometry of matroids. We describe its combinatorial structure, showing that it is a (2n−2)-dimensional polytope with (n!)2(1+12+⋯+1n) vertices and 3n−3 facets. We also give a formula for its volume: it is a weighted sum of the degrees of the projective varieties of all the toric ideals of connected bipartite graphs with n edges; or equivalently, a weighted sum of the lattice point counts of all the corresponding trimmed generalized permutahedra.