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Article overview
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Proof of a conjecture on unimodality | Yi Wang
; Yeong-Nan Yeh
; | Date: |
9 Sep 2008 | 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
$lceil{m-dover d+1}
ceil$. | Source: | arXiv, 0809.1586 | Services: | Forum | Review | PDF | Favorites |
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