Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con