Positroids, non-crossing partitions, and positively oriented matroids - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2014

Positroids, non-crossing partitions, and positively oriented matroids


We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely by choosing a non-crossing partition on the ground set, and then freely placing the structure of a connected positroid on each of the blocks of the partition. We use this to enumerate connected positroids, and we prove that the probability that a positroid on [n] is connected equals $1/e^2$ asymptotically. We also prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from this result that the positive matroid Grassmannian (or positive MacPhersonian) is homeomorphic to a closed ball.
Fichier principal
Vignette du fichier
dmAT0157.pdf (371.77 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01207540 , version 1 (01-10-2015)



Federico Ardila, Felipe Rincón, Lauren Williams. Positroids, non-crossing partitions, and positively oriented matroids. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.655-666, ⟨10.46298/dmtcs.2431⟩. ⟨hal-01207540⟩


269 View
772 Download



Gmail Facebook Twitter LinkedIn More