Arrangements of equal minors in the positive Grassmannian by Miriam Farber, Alexander Postnikov

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Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex by Miriam Farber, Yelena Mandelshtam

“…The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. …”
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Weak Separation, Pure Domains and Cluster Distance by Miriam Farber, Pavel Galashin

“…We apply our result to calculate the cluster distance and to give lower bounds on the mutation distance between cluster variables in the cluster algebra structure on the coordinate ring of the Grassmannian. Using a linear projection that relates weak separation to the octahedron recurrence, we also find the exact mutation distances and cluster distances for a family of cluster variables.…”
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