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The Rank Function of a Positroid and Non-Crossing Partitions

2020; Electronic Journal of Combinatorics; Volume: 27; Issue: 1 Linguagem: Inglês

10.37236/8256

1097-1440

Robert Mcalmon, Suho Oh,

DNA and Biological Computing

A positroid is a special case of a realizable matroid, that arose from the study of totally nonnegative part of the Grassmannian by Postnikov. 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. 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.