Log concavity of $(1+x)^m (1+ x^k)$

Details Log concavity of $(1+x)^m (1+ x^k)$ Log concavity of $(1+x)^m (1+ x^k)$

2011-02-15

arxiv.org/abs/1102.2961v1

Mathematics

Combinatorics

Scientific paper

Let $P$ be the polynomial of the title, with $m$ and $k$ integers. Then $P$
is strongly unimodal (that is, its sequence of coefficients is log concave) if
and only if $m \geq k^2 -3$ if and only if $P$ has unimodal coefficients. We
also show that in order to satisfy a condition concerning its behaviour on the
unit circle, we must have $m$ of order $k^4$ or more.

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