McAlmon, RobertOh, Suho2020-03-032020-03-032020-01-10McAlmon, R. & Oh, S. (2020). The rank function of a positroid and non-crossing partitions. Electronic Journal of Combinatorics, 27(1).1077-8926https://hdl.handle.net/10877/9344A 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.Text13 pages1 file (.pdf)enrealizable matroidpositroidMathematicsArticle© Robert Mcalmon and Suho Oh.https://doi.org/10.37236/8256This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.