Séminaire Lotharingien de Combinatoire, 80B.68 (2018), 12 pp.

Pavel Galashin

Plabic Graphs and Zonotopal Tilings

Abstract. We introduce the notion of chord separation of two sets which generalizes Leclerc and Zelevinsky's weak separation. We show that every maximal by inclusion collection of pairwise chord separated sets is also maximal by size. Moreover, we prove that such collections are in bijection with fine zonotopal tilings of the three-dimensional cyclic zonotope. As a result, we get that Postnikov's reduced plabic graphs are precisely the objects dual to horizontal sections of zonotopal tilings of the three-dimensional cyclic zonotope, and Postnikov's moves on plabic graphs correspond to flips of these zonotopal tilings.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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