Triangulations of Oriented Matroids

Released on by Francisco Santos
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  • Triangulations of Oriented Matroids Book Detail

  • Author : Francisco Santos
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 95
  • ISBN 13 : 0821827693
  • File Size : 57,57 MB
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Triangulations of Oriented Matroids by Francisco Santos PDF Summary

Book Description: We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.

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Triangulations of Oriented Matroids

Triangulations of Oriented Matroids

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We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson a

Oriented Matroids

Oriented Matroids

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First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.