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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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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
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Right arrow How to cite this article
Google Scholar
Right arrow Articles by Talaska, K.
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What's this?