Geodesic
Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstract
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

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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. 
@article{DMTCS_2009_special_256_a28,
     author = {Talaska, Kelli},
     title = {Combinatorial formulas for ⅃-coordinates in a totally nonnegative {Grassmannian,} extended abstract, extended abstract},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2706},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2706/}
}
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%T Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstract
%J Discrete mathematics & theoretical computer science
%D 2009
%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
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Talaska, Kelli. Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstract. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2706. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2706/

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