All Title Author
Keywords Abstract

Mathematics  2015 

Combinatorics of symmetric plabic graphs

Full-Text   Cite this paper   Add to My Lib

Abstract:

A plabic graph is a planar bicolored graph embedded in a disk, which satisfies some combinatorial conditions. Postnikov's boundary measurement map takes the space of positive edge weights of a plabic graph $G$ to a positroid cell in $\text{Gr}_{\geq 0}(k,n)$. In this note, we investigate plabic graphs which are symmetric about a line of reflection, up to reversing the colors of vertices. These symmetric plabic graphs arise naturally in the study of total positivity for the Lagrangian Grassmannian. We characterize various combinatorial objects associated with symmetric plabic graphs, and describe the subset of $\text{Gr}_{\geq 0}(k,n)$ which can be realized by symmetric weightings of symmetric plabic graphs.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal