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2011

Weak Separation and Plabic Graphs

Oh, Suho, Postnikov, Alex, Speyer, David E

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Leclerc and Zelevinsky described quasicommuting families of quantum minors in terms of a certain combinatorial condition, called weak separation.

They conjectured that all maximal by inclusion weakly separated collections of minors have the same cardinality, and that they can be related to each other by a sequence of mutations.
On the other hand, Postnikov studied total positivity on the Grassmannian.
He described a stratification of the totally nonnegative Grassmannian into positroid strata, and constructed their parametrization using plabic graphs.

Weak Separation and Plabic Graphs · Around

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Constructions
Thomas Brylawski · 1986
Earlier work this paper cites.
Quasicommuting families of quantum Plücker coordinates
Bernard Leclerc and Andrei Zelevinsky · 1998
Earlier work this paper cites.
Noncrossing partitions
Rodica Simion · 2000
Earlier work this paper cites.
Quantum Cluster Algebras
Arkady Berenstein and Andrei Zelevinsky · 2005
Earlier work this paper cites.

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