# Subword complexes via triangulations of root polytopes

Authors
Type
Preprint
Publication Date
Feb 25, 2015
Submission Date
Feb 13, 2015
Identifiers
arXiv ID: 1502.03997
Source
arXiv
Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. We show that a family of subword complexes can be realized geometrically via regular triangulations of root polytopes. This implies that a family of $\beta$-Grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. We can also write the volume and Ehrhart series of root polytopes in terms of $\beta$-Grothendieck polynomials.