Subword complexes via triangulations of root polytopes

Escobar, Laura¹ ; Mészáros, Karola²

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

Algebraic Combinatorics, Tome 1 (2018) no. 3, pp. 395-414.

Résumé

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.

Détail

Reçu le : 2017-12-08
Accepté le : 2018-03-07
Publié le : 2018-06-28
DOI : 10.5802/alco.17

Classification : 52B20, 05E45
Keywords: subword complex, pipedream, triangulation, root polytope

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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