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Positroids and Schubert matroids. (English) Zbl 1231.05061

Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroid. In this paper author proves his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a nice combinatorial description of positroids that is easily computable.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
14M15 Grassmannians, Schubert varieties, flag manifolds
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References:

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