2015/02/13 by Escobar, Laura, Mészáros, Karola
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1502.03997
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 β-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 β-Grothendieck polynomials.