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arXiv · 1502.03997

Subword complexes via triangulations of root polytopes

Laura Escobar·Karola Mészáros
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Abstract

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.

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Laura Escobar, Karola Mészáros. 2015-02-13. Subword complexes via triangulations of root polytopes. https://arxiv.org/abs/1502.03997

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