Counting weighted maximal chains in the circular Bruhat order
Abstract
The totally nonnegative Grassmannian Gr(k,n)≥0 is the subset of the real Grassmannian Gr(k,n) consisting of points with all nonnegative Pl\"ucker coordinates. The circular Bruhat order is a poset isomorphic to the face poset of A. Postnikov's (2005) positroid cell decomposition of Gr(k,n)≥0. We provide a closed formula for the sum of its weighted chains in the spirit of J. Stembridge (2002).
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