# Vector-relation configurations and plabic graphs

@article{Affolter2019VectorrelationCA, title={Vector-relation configurations and plabic graphs}, author={Niklas C. Affolter and Max Glick and P. Pylyavskyy and Sanjay Ramassamy}, journal={arXiv: Combinatorics}, year={2019} }

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… CONTINUE READING

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