Total positivity, Grassmannians, and networks

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dc.creatorPostnikov, Alexander
dc.date2006-09-27
dc.date.accessioned2026-07-07T07:25:19Z
dc.date.available2026-07-07T07:25:19Z
dc.descriptionThe aim of this paper is to discuss a relationship between total positivity and planar directed networks. We show that the inverse boundary problem for these networks is naturally linked with the study of the totally nonnegative Grassmannian. We investigate its cell decomposition, where the cells are the totally nonnegative parts of the matroid strata. The boundary measurements of networks give parametrizations of the cells. We present several different combinatorial descriptions of the cells, study the partial order on the cells, and describe how they are glued to each other.
dc.description79 pages
dc.identifierhttps://arxiv.org/abs/math/0609764
dc.identifierhttp://arxiv.org/abs/math/0609764
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116676
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleTotal positivity, Grassmannians, and networks
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