English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper we use toric geometry to investigate the topology of thetotally non-negative part of the Grassmannian (Gr_{kn})_{\geq 0}. This is acell complex whose cells Delta_G can be parameterized in terms of thecombinatorics of plane-bipartite graphs G. To each cell Delta_G we associate acertain polytope P(G). The polytopes P(G) are analogous to the well-knownBirkhoff polytopes, and we describe their face lattices in terms of matchingsand unions of matchings of G. We also demonstrate a close connection betweenthe polytopes P(G) and matroid polytopes. We then use the data of P(G) todefine an associated toric variety X_G. We use our technology to prove that thecell decomposition of (Gr_{kn})_{\geq 0} is a CW complex, and furthermore, thatthe Euler characteristic of the closure of each cell of (Gr_{kn})_{\geq 0} is1.

Matching polytopes, toric geometry, and the non-negative part of the Grassmannian