Counting weighted maximal chains in the circular Bruhat order

Gopal Goel; Olivia McGough; David Perkinson

Counting weighted maximal chains in the circular Bruhat order

Combinatorics 2021-08-10 v1

Authors: Gopal Goel , Olivia McGough , David Perkinson

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 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).

Keywords

grassmannian varieties

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@article{arxiv.2108.03504,
  title  = {Counting weighted maximal chains in the circular Bruhat order},
  author = {Gopal Goel and Olivia McGough and David Perkinson},
  journal= {arXiv preprint arXiv:2108.03504},
  year   = {2021}
}

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8 pages

Counting weighted maximal chains in the circular Bruhat order

Abstract

Keywords

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