Combinatorial formulas for Le-coordinates in a totally nonnegative Grassmannian

Details Combinatorial formulas for Le-coordinates in a totally nonnegative Grassmannian Combinatorial formulas for Le-coordinates in a totally nonnegative Grassmannian

2008-12-03

arxiv.org/abs/0812.0640v2

Mathematics

Combinatorics

11 pages, 5 figures; v2: Minor revisions throughout, some simplified proofs

Scientific paper

Postnikov constructed a decomposition of a totally nonnegative Grassmannian into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point belongs to and to determine affine coordinates of the point within this cell. This simplifies Postnikov's description of the inverse boundary measurement map and generalizes formulas for the top cell given by Speyer and Williams. In addition, we identify a particular subset of Pluecker coordinates as a totally positive base for the set of non-vanishing Pluecker coordinates for a given positroid cell.

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