The Rank Function of a Positroid and Non-Crossing Partitions
dc.contributor.author | McAlmon, Robert | |
dc.contributor.author | Oh, Suho | |
dc.date.accessioned | 2020-03-03T20:17:55Z | |
dc.date.available | 2020-03-03T20:17:55Z | |
dc.date.issued | 2020-01 | |
dc.description.abstract | A 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.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 13 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | McAlmon, R. & Oh, S. (2020). The rank function of a positroid and non-crossing partitions. Electronic Journal of Combinatorics, 27(1). | |
dc.identifier.doi | https://doi.org/10.37236/8256 | |
dc.identifier.issn | 1077-8926 | |
dc.identifier.uri | https://hdl.handle.net/10877/9344 | |
dc.language.iso | en | |
dc.publisher | Electronic Journal of Combinatorics | |
dc.rights.holder | © Robert Mcalmon and Suho Oh. | |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License. | |
dc.source | Electronic Journal of Combinatorics, 2020, Vol. 27, No. 1. | |
dc.subject | realizable matroid | |
dc.subject | positroid | |
dc.title | The Rank Function of a Positroid and Non-Crossing Partitions | |
dc.type | Article |
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