Tropicalization, symmetric polynomials, and complexity
Combinatorics
2020-06-02 v1 Computational Complexity
Abstract
D. Grigoriev-G. Koshevoy recently proved that tropical Schur polynomials have (at worst) polynomial tropical semiring complexity. They also conjectured tropical skew Schur polynomials have at least exponential complexity; we establish a polynomial complexity upper bound. Our proof uses results about (stable) Schubert polynomials, due to R. P. Stanley and S. Billey-W. Jockusch-R. P. Stanley, together with a sufficient condition for polynomial complexity that is connected to the saturated Newton polytope property.
Cite
@article{arxiv.1710.03312,
title = {Tropicalization, symmetric polynomials, and complexity},
author = {Alexander Woo and Alexander Yong},
journal= {arXiv preprint arXiv:1710.03312},
year = {2020}
}
Comments
8 pages