Subword complexes via triangulations of root polytopes
Algebraic Combinatorics, Volume 1 (2018) no. 3, p. 395-414
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.
Received : 2017-12-08
Accepted : 2018-03-07
Published online : 2018-06-28
DOI : https://doi.org/10.5802/alco.17
Classification:  52B20,  05E45
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},
     publisher = {MathOA foundation},
     volume = {1},
     number = {3},
     year = {2018},
     pages = {395-414},
     doi = {10.5802/alco.17},
     language = {en},
     url = {http://alco.centre-mersenne.org/item/ALCO_2018__1_3_395_0}
}
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. https://alco.centre-mersenne.org/item/ALCO_2018__1_3_395_0/

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