Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstractReportar como inadecuado




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1 Department of Mathematics - University of Michigan

Abstract : Postnikov constructed a decomposition of a totally nonnegative Grassmannian $Gr {kn} ≥0$ into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point in $Gr {kn} ≥0$ 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 Plücker coordinates as a totally positive base for the set of non-vanishing Plücker coordinates for a given positroid cell.

Keywords : positroid totally nonnegative Grassmannian Le-diagram





Autor: Kelli Talaska -

Fuente: https://hal.archives-ouvertes.fr/



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