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 -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 -Grothendieck polynomials.
Accepted:
Published online:
DOI: 10.5802/alco.17
Keywords: subword complex, pipedream, triangulation, root polytope
@article{ALCO_2018__1_3_395_0, author = {Escobar, Laura and M\'esz\'aros, Karola}, title = {Subword complexes via triangulations of root polytopes}, journal = {Algebraic Combinatorics}, pages = {395--414}, publisher = {MathOA foundation}, volume = {1}, number = {3}, year = {2018}, doi = {10.5802/alco.17}, zbl = {1393.52010}, mrnumber = {3856530}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.17/} }
TY - JOUR AU - Escobar, Laura AU - Mészáros, Karola TI - Subword complexes via triangulations of root polytopes JO - Algebraic Combinatorics PY - 2018 SP - 395 EP - 414 VL - 1 IS - 3 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.17/ DO - 10.5802/alco.17 LA - en ID - ALCO_2018__1_3_395_0 ER -
Escobar, Laura; Mészáros, Karola. Subword complexes via triangulations of root polytopes. Algebraic Combinatorics, Volume 1 (2018) no. 3, pp. 395-414. doi : 10.5802/alco.17. http://archive.numdam.org/articles/10.5802/alco.17/
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