On Plücker coordinates of a perfectly oriented planar network - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2008

On Plücker coordinates of a perfectly oriented planar network

Abstract

Let $G$ be a perfectly oriented planar graph. Postnikov's boundary measurement construction provides a rational map from the set of positive weight functions on the edges of $G$ onto the appropriate totally nonnegative Grassmann cell. We establish an explicit combinatorial formula for Postnikov's map by expressing each Plücker coordinate of the image as a ratio of two polynomials in the edge weights, with positive integer coefficients. These polynomials are weight generating functions for certain subsets of edges in $G$.
Fichier principal
Vignette du fichier
dmAJ0150.pdf (53.11 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01185150 , version 1 (19-08-2015)

Identifiers

Cite

Kelli Talaska. On Plücker coordinates of a perfectly oriented planar network. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.583-586, ⟨10.46298/dmtcs.3616⟩. ⟨hal-01185150⟩

Collections

INSMI TDS-MACS
37 View
454 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More