# ALGEBRAIC COMBINATORICS

Subword complexes via triangulations of root polytopes
Algebraic Combinatorics, Volume 1 (2018) no. 3, pp. 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 $\beta$-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.

Accepted:
Published online:
DOI: 10.5802/alco.17
Classification: 52B20,  05E45
Keywords: subword complex, pipedream, triangulation, root polytope
Escobar, Laura 1; Mészáros, Karola 2

1 University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 W. Green Street, Urbana, IL 61801, USA
2 Cornell University, Department of Mathematics, 310 Malott Hall, Ithaca, NY 14850, USA
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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/articles/10.5802/alco.17/

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