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{\bf Donna Q. J. Dou and Arthur L. B. Yang}
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{\bf On the Modes of Polynomials Derived from Nondecreasing Sequences}
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Wang and Yeh proved that if $P(x)$ is a polynomial with nonnegative
and nondecreasing coefficients, then $P(x+d)$ is unimodal for any
$d>0$. A mode of a unimodal polynomial $f(x)=a_0+a_1x+\cdots + a_mx^m$
is an index $k$ such that $a_k$ is the maximum coefficient.  Suppose
that $M_*(P,d)$ is the smallest mode of $P(x+d)$, and $M^*(P,d)$ the
greatest mode. Wang and Yeh conjectured that if $d_2>d_1>0$, then
$M_*(P,d_1)\geq M_*(P,d_2)$ and $M^*(P,d_1)\geq M^*(P,d_2)$. We give a
proof of this conjecture.



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