The Rank Function of a Positroid and Non-Crossing Partitions

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dc.contributor.authorMcAlmon, Robert
dc.contributor.authorOh, Suho
dc.date.accessioned2020-03-03T20:17:55Z
dc.date.available2020-03-03T20:17:55Z
dc.date.issued2020-01-10
dc.description.abstractA positroid is a special case of a realizable matroid that arose from the study of totally nonnegative part of the Grassmannian by Postnikov [13]. Postnikov demonstrated that positroids are in bijection with certain interesting classes of combinatorial objects, such as Grassmann necklaces and decorated permutations. The bases of a positroid can be described directly in terms of the Grassmann necklace and decorated permutation [10]. In this paper, we show that the rank of an arbitrary set in a positroid can be computed directly from the associated decorated permutation using non-crossing partitions.
dc.description.departmentMathematics
dc.formatText
dc.format.extent13 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationMcAlmon, R. & Oh, S. (2020). The rank function of a positroid and non-crossing partitions. Electronic Journal of Combinatorics, 27(1).
dc.identifier.doihttps://doi.org/10.37236/8256
dc.identifier.issn1077-8926
dc.identifier.urihttps://hdl.handle.net/10877/9344
dc.language.isoen
dc.publisherElectronic Journal of Combinatorics
dc.rights.holder© Robert Mcalmon and Suho Oh.
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
dc.sourceElectronic Journal of Combinatorics, 2020, Vol. 27, No. 1.
dc.subjectrealizable matroid
dc.subjectpositroid
dc.subjectMathematics
dc.titleThe Rank Function of a Positroid and Non-Crossing Partitions
dc.typeArticle

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