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Combinatorics of Positroids

Suho Oh 1
1 Department of Mathematics [MIT]
Abstract : Recently Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroids. There are many interesting combinatorial objects associated to a positroid. We introduce some recent results, including the generalization and proof of the purity conjecture by Leclerc and Zelevinsky on weakly separated sets.
Keywords : Positroids Total positivity Grassmannian Matroids $\rfloor$-diagrams Decorated permutations Weakly separated.
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Suho Oh. Combinatorics of Positroids. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.721-732. ⟨hal-01185389⟩

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