A formula for Plücker coordinates associated with a planar network

dc.creatorTalaska, Kelli
dc.date2008-01-31
dc.date2008-04-15
dc.date.accessioned2026-07-07T10:03:22Z
dc.date.available2026-07-07T10:03:22Z
dc.descriptionFor a planar directed graph G, Postnikov's boundary measurement map sends positive weight functions on the edges of G onto the appropriate totally nonnegative Grassmann cell. We establish an explicit formula for Postnikov's map by expressing each Pluecker 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 Pluecker coordinates.
dc.description15 pages, 6 figures. Extensive additions, including a generalization for arbitrarily oriented planar graphs and a formula for some Pluecker coordinates of non-planar perfectly oriented graphs
dc.identifierhttps://arxiv.org/abs/0801.4822
dc.identifierhttp://arxiv.org/abs/0801.4822
dc.identifierInt Math Res Notices (2008) Vol. 2008, article ID rnn081, 19 pages, published on July 24, 2008.
dc.identifierdoi:10.1093/imrn/rnn081
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169265
dc.subjectCombinatorics
dc.subjectRings and Algebras
dc.subject15A48 (Primary); 05A15 (Secondary)
dc.titleA formula for Plücker coordinates associated with a planar network
dc.typetext

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