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arXiv · 0809.1586

Proof of a conjecture on unimodality

Yi Wang·Yeong-Nan Yeh
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Abstract

Let $P(x)$ be a polynomial of degree $m$, with nonnegative and non-decreasing coefficients. We settle the conjecture that for any positive real number $d$, the coefficients of $P(x+d)$ form a unimodal sequence, of which the special case $d$ being a positive integer has already been asserted in a previous work. Further, we explore the location of modes of $P(x+d)$ and present some sufficient conditions on $m$ and $d$ for which $P(x+d)$ has the unique mode $\lceil{m-d\over d+1}\rceil$.

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Yi Wang, Yeong-Nan Yeh. 2008-09-09. Proof of a conjecture on unimodality. https://arxiv.org/abs/0809.1586

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