Counting weighted maximal chains in the circular Bruhat order
Abstract
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 Plücker 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).
- Publication:
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arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- arXiv:
- arXiv:2108.03504
- Bibcode:
- 2021arXiv210803504G
- Keywords:
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- Mathematics - Combinatorics;
- 05E15 (Primary) 05A15 (Secondary)
- E-Print:
- 8 pages