Counting weighted maximal chains in the circular Bruhat order
The totally nonnegative Grassmannian $\mathrm{Gr}(k,n)_{\geq0}$ is the subset of the real Grassmannian $\mathrm{Gr}(k,n)$ 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 ce...
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| Zusammenfassung: | The totally nonnegative Grassmannian $\mathrm{Gr}(k,n)_{\geq0}$ is the subset
of the real Grassmannian $\mathrm{Gr}(k,n)$ 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 $\mathrm{Gr}(k,n)_{\geq0}$. We provide a closed formula for
the sum of its weighted chains in the spirit of J. Stembridge (2002). |
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| DOI: | 10.48550/arxiv.2108.03504 |