The Rank Function of a Positroid and Non-Crossing Partitions
Date
2020-01-10
Authors
McAlmon, Robert
Oh, Suho
Journal Title
Journal ISSN
Volume Title
Publisher
Electronic Journal of Combinatorics
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.
Description
Keywords
realizable matroid, positroid, Mathematics
Citation
McAlmon, R. & Oh, S. (2020). The rank function of a positroid and non-crossing partitions. Electronic Journal of Combinatorics, 27(1).
Rights
Rights Holder
© Robert Mcalmon and Suho Oh.
Rights License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.