Counting weighted maximal chains in the circular Bruhat order

The totally nonnegative Grassmannian Gr(k, n)(>= 0) is the subset of the real Grassmannian Gr(k, n) consisting of points with all nonnegative Plucker coordinates. The circular Bruhat order is a poset isomorphic to the face poset of Postnikov's positroid cell decomposition of Gr(k, n)(>= 0) [10]. We provide a closed formula for the sum of its weighted chains in the spirit of Stembridge [11]. (c) 2022 Elsevier Inc. All rights reserved.