Coefficients and Roots of Peak Polynomials

@article{Billey2016CoefficientsAR,
title={Coefficients and Roots of Peak Polynomials},
author={Sara C. Billey and Matthew Fahrbach and Alan Talmage},
journal={Experimental Mathematics},
year={2016},
volume={25},
pages={165 - 175}
}
• Published 30 October 2014
• Mathematics, Computer Science
• Experimental Mathematics
ABSTRACT Given a permutation , we say an index i is a peak if πi − 1 < πi > πi + 1. Let P(π) denote the set of peaks of π. Given any set S of positive integers, define . Billey–Burdzy–Sagan showed that for all fixed subsets of positive integers S and sufficiently large n, for some polynomial pS(x) depending on S. They conjectured that the coefficients of pS(x) expanded in a binomial coefficient basis centered at max (S) are all positive. We show that this is a consequence of a stronger… Expand
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