• Mathematics
  • Published 2007

MATCHING POLYTOPES, TORIC GEOMETRY, AND THE NON-NEGATIVE PART OF THE GRASSMANNIAN

@inproceedings{Postnikov2007MATCHINGPT,
  title={MATCHING POLYTOPES, TORIC GEOMETRY, AND THE NON-NEGATIVE PART OF THE GRASSMANNIAN},
  author={Alexander Postnikov and David Speyer and Lauren Kelly Williams},
  year={2007}
}
In this paper we use toric geometry to investigate the topology of the totally non-negative part of the Grassmannian (Grkn)�0. (Grkn)�0 is a cell complex whose cellsG can be parameterized in terms of the combina- torics of bicolored planar graphs G. To each cellG we associate a complete fan FG which is normal to a certain polytope P(G). The combinatorial struc- ture of the polytopes P(G) is reminiscent of the well-known Birkhoff polytopes, and we describe their face lattices in terms of… CONTINUE READING

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