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Tr. Mat. Inst. Steklova, 2014, Volume 286, Pages 129–143 (Mi tm3569)  

This article is cited in 2 scientific papers (total in 2 papers)

Subword complexes and edge subdivisions

M. A. Gorskyab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Université Paris Diderot — Paris 7, Institut de Mathématiques de Jussieu — Paris Rive Gauche, UMR 7586 du CNRS, Paris, France

Abstract: For a finite Coxeter group, a subword complex is a simplicial complex associated with a pair $(\mathbf Q,\pi)$, where $\mathbf Q$ is a word in the alphabet of simple reflections and $\pi$ is a group element. We discuss the transformations of such a complex that are induced by braid moves of the word $\mathbf Q$. We show that under certain conditions, such a transformation is a composition of edge subdivisions and inverse edge subdivisions. In this case, we describe how the $H$- and $\gamma$-polynomials change under the transformation. This case includes all braid moves for groups with simply laced Coxeter diagrams.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-92612
The work was supported by DIM RDM-IdF of the Region Ile-de-France and by the Russian Foundation for Basic Research (project no. 14-01-92612-KO).


DOI: https://doi.org/10.1134/S0371968514030078

Full text: PDF file (246 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 286, 114–127

Bibliographic databases:

Document Type: Article
UDC: 514.172.45
Received in December 2013

Citation: M. A. Gorsky, “Subword complexes and edge subdivisions”, Algebraic topology, convex polytopes, and related topics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 286, MAIK Nauka/Interperiodica, Moscow, 2014, 129–143; Proc. Steklov Inst. Math., 286 (2014), 114–127

Citation in format AMSBIB
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\by M.~A.~Gorsky
\paper Subword complexes and edge subdivisions
\inbook Algebraic topology, convex polytopes, and related topics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 286
\pages 129--143
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    This publication is cited in the following articles:
    1. T. McConville, “Lattice structure of grid-Tamari orders”, J. Comb. Theory Ser. A, 148 (2017), 27–56  crossref  mathscinet  zmath  isi  scopus
    2. T. Manneville, “Fan realizations for some 2-associahedra”, Exp. Math., 27:4 (2018), 377–394  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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