A new vector-relation framework on bipartite graphs unifies several discrete integrable systems and proves unique reconstruction from boundary data for plabic graphs.
Positive Grassmannian and polyhedral subdivisions
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as positroids and plabic graphs. Remarkably, the same combinatorial structures appeared in many other areas of mathematics and physics, e.g., in the study of cluster algebras, scattering amplitudes, and solitons. We discuss new ways to think about these structures. In particular, we identify plabic graphs and more general Grassmannian graphs with polyhedral subdivisions induced by 2-dimensional projections of hypersimplices. This implies a close relationship between the positive Grassmannian and the theory of fiber polytopes and the generalized Baues problem. This suggests natural extensions of objects related to the positive Grassmannian.
fields
math.CO 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Vector-relation configurations and plabic graphs
A new vector-relation framework on bipartite graphs unifies several discrete integrable systems and proves unique reconstruction from boundary data for plabic graphs.