Principal specializations of Schubert polynomials and pattern containment

Yibo Gao

Principal specializations of Schubert polynomials and pattern containment

Combinatorics 2019-10-22 v1

Authors: Yibo Gao

Abstract

We show that the principal specialization of the Schubert polynomial at $w$ is bounded below by $1+p_{132}(w)+p_{1432}(w)$ where $p_u(w)$ is the number of occurrences of the pattern $u$ in $w$ , strengthening a previous result by A. Weigandt. We then make a conjecture relating the principal specialization of Schubert polynomials to pattern containment. Finally, we characterize permutations $w$ whose RC-graphs are connected by simple ladder moves via pattern avoidance.

Keywords

schubert polynomials polynomial theory polynomial roots

Cite

@article{arxiv.1910.08872,
  title  = {Principal specializations of Schubert polynomials and pattern containment},
  author = {Yibo Gao},
  journal= {arXiv preprint arXiv:1910.08872},
  year   = {2019}
}

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