Séminaire Lotharingien de Combinatoire, 82B.43 (2019), 12 pp.

Robert Mcalmon, Suho Oh, and David Xiang

Flats of a positroid from its decorated permutation

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. 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 extended abstract, we show how to describe the flats, bases and independent sets directly from the decorated permutation, bypassing the use of the Grassmann necklace.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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