Counting weighted maximal chains in the circular Bruhat order
JOURNAL OF COMBINATORIAL THEORY SERIES A(2023)
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 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.
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Key words
Circular Bruhat order,k-Bruhat order,Positroid,Totally nonnegative Grassmannian
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