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      Chapter

      Minimal Generalized Galleries in a Coxeter Complex
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      Chapter

      Minimal Generalized Galleries in a Coxeter Complex

      DOI link for Minimal Generalized Galleries in a Coxeter Complex

      Minimal Generalized Galleries in a Coxeter Complex book

      Minimal Generalized Galleries in a Coxeter Complex

      DOI link for Minimal Generalized Galleries in a Coxeter Complex

      Minimal Generalized Galleries in a Coxeter Complex book

      ByCarlos Contou-Carrère
      BookBuildings and Schubert Schemes

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      Edition 1st Edition
      First Published 2016
      Imprint CRC Press
      Pages 54
      eBook ISBN 9781315367309
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      ABSTRACT

      This chapter introduces the minimal generalized galleries in the setting of Coxeter complexes. The existence of minimal generalized galleries is proven by means of the geometrical realization of a Coxeter Complex as a decomposition of an euclidean space by simplicial cones. A unicity result about generalized galleries with associated minimal galleries of types, i.e. galleries of types defined by minimal generalized galleries, is proven. An expression of the convex hull of two facets is obtained. It allows one to prove that a Minimal Generalized Gallery is contained in the convex hull of its extremities. The chapter describes the type of relative position associated to Minimal Generalized Galleries of types. The correspondence between Minimal Generalized Galleries issued from a chamber C and a set of words in is extended to a correspondence between the generalized galleries issued from C and words in a set larger than.

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