2015/10/07 by Rachel Karpman, Yi Su, Karpman, Rachel +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.1510.02122
openalex publication_date 2015/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 some totally nonnegative Grassmannian. 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 a Grassmannian which can be realized by symmetric weightings of symmetric plabic graphs.