Tropicalization, symmetric polynomials, and complexity. (July 2020)

• Record Type: Journal Article
• Authors: Woo, Alexander; Yong, Alexander
• Is Part Of: Journal of symbolic computation. Volume 99(2020)
• Page Start: 242
• Page End: 249
• Publication Date: 2020-07
• Subjects: Tropical semiring complexity -- Schur polynomials; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.06.002
• Languages: English
• ISSNs: 0747-7171

Abstract

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.