Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775351 | Advances in Applied Mathematics | 2018 | 24 Pages |
Abstract
Franco, Galloni, Penante, and Wen have proposed a boundary measurement map for a graph on any closed orientable surface with boundary. We consider this boundary measurement map which takes as input an edge weighted directed graph embedded on a surface and produces on element of a Grassmannian. Computing the boundary measurement requires a choice of fundamental domain. Here the boundary measurement map is shown to be independent of the choice of fundamental domain Also, a formula for the Plücker coordinates of the element of the Grassmannian in the image of the boundary measurement map is given. The formula expresses the Plücker coordinates as a rational function which can be combinatorially described in terms of paths and cycles in the directed graph.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
John Machacek,