Subword complexes via triangulations of root polytopes

摘要: Subword complexes are simplicial introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials determinantal ideals. They proved that any subword complex is homeomorphic a ball or sphere asked about their geometric realizations. We show family can be realized geometrically via regular triangulations root polytopes. This implies $\beta$-Grothendieck special cases reduced forms in subdivision algebra also write volume Ehrhart series polytopes terms polynomials.