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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn081, 19 pages, doi:10.1093/imrn/rnn081 published on July 24, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

A Formula for Plücker Coordinates Associated with a Planar Network

Kelli Talaska

Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA

Correspondence: Correspondence to be sent to: kellicar{at}umich.edu

For a planar directed graph G, Postnikov's boundary measurement map sends positive weight functions on the edges of G onto the appropriate totally non-negative Grassmann cell. We establish an explicit formula for Postnikov's map by expressing each Plücker coordinate as a ratio of two combinatorially defined polynomials in the edge weights, with positive integer coefficients. In the non-planar setting, we show that a similar formula holds for special choices of Plücker coordinates.


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