Weighted counting of Bruhat paths by shifted $R$-polynomials
Combinatorics
2019-07-30 v1
Abstract
We revisit -polynomials with introducing the new idea ``shifted -polynomials" (or Bruhat weight) for all Bruhat intervals in finite Coxeter groups. Then, we apply these polynomials to weighted counting of Bruhat paths. Further, we prove a new criterion of irregularity of lower intervals as analogy of Carrell-Peterson's and Dyer's results. Also, we present the upper bound of shifted -polynomials for Bruhat intervals of fixed length by Jacobsthal numbers.
Cite
@article{arxiv.1907.11802,
title = {Weighted counting of Bruhat paths by shifted $R$-polynomials},
author = {Masato Kobayashi},
journal= {arXiv preprint arXiv:1907.11802},
year = {2019}
}
Comments
26 pages, 3 figures, 2 tables