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dc.contributor.authorOh, S.
dc.contributor.authorSpeyer, D. E.
dc.contributor.authorPostnikov, Alexander
dc.date.accessioned2017-01-12T19:36:14Z
dc.date.available2017-01-12T19:36:14Z
dc.date.issued2015-02
dc.date.submitted2014-03
dc.identifier.issn0024-6115
dc.identifier.issn1460-244X
dc.identifier.urihttp://hdl.handle.net/1721.1/106463
dc.description.abstractLeclerc and Zelevinsky described quasicommuting families of quantum minors in terms of a certain combinatorial condition, called weak separation. They conjectured that all inclusion-maximal weakly separated collections of minors have the same cardinality, and that they can be related to each other by a sequence of mutations. Postnikov studied total positivity on the Grassmannian. He described a stratification of the totally non-negative Grassmannian into positroid strata, and constructed theirparameterization using plabic graphs. In this paper, we link the study of weak separation to plabic graphs. We extend the notion of weak separation to positroids. We generalize the conjectures of Leclerc and Zelevinsky, and related ones of Scott, and prove them. We show that the maximal weakly separated collections in a positroid are in bijective correspondence with the plabic graphs. This correspondence allows us to use the combinatorial techniques of positroids and plabic graphs to prove the (generalized) purity and mutation connectedness conjectures.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (CAREER Award DMS-0504629)en_US
dc.language.isoen_US
dc.publisherOxford University Press - London Mathematical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1112/plms/pdu052en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleWeak separation and plabic graphsen_US
dc.typeArticleen_US
dc.identifier.citationOh, Suho, Alexander Postnikov, and David E. Speyer. “Weak Separation and Plabic Graphs.” Proceedings of the London Mathematical Society 110.3 (2015): 721–754.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorPostnikov, Alexander
dc.relation.journalProceedings of the London Mathematical Societyen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsOh, S.; Postnikov, A.; Speyer, D. E.en_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-3964-8870
mit.licenseOPEN_ACCESS_POLICYen_US


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