Vector-relation configurations and plabic graphs - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Vector-relation configurations and plabic graphs


We study a simple geometric model for local transformations of bipartite graphs. The state consists of a choice of a vector at each white vertex made in such a way that the vectors neighboring each black vertex satisfy a linear relation. Evolution for different choices of the graph coincides with many notable dynamical systems including the pentagram map, Q-nets, and discrete Darboux maps. On the other hand, for plabic graphs we prove unique extendability of a configuration from the boundary to the interior, an elegant illustration of the fact that Postnikov's boundary measurement map is invertible. In all cases there is a cluster algebra operating in the background, resolving the open question for Q-nets of whether such a structure exists.
Fichier principal
Vignette du fichier
Vectors and relations on bipartite graphs.pdf (496.82 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02595570 , version 1 (15-05-2020)


  • HAL Id : hal-02595570 , version 1


Niklas Affolter, Max Glick, Pavlo Pylyavskyy, Sanjay Ramassamy. Vector-relation configurations and plabic graphs. 2020. ⟨hal-02595570⟩
39 View
32 Download


Gmail Facebook Twitter LinkedIn More