Proof of a conjecture on unimodality
| dc.creator | Wang, Yi | |
| dc.creator | Yeh, Yeong-Nan | |
| dc.date | 2008-09-09 | |
| dc.date.accessioned | 2026-07-07T10:01:46Z | |
| dc.date.available | 2026-07-07T10:01:46Z | |
| dc.description | 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 $\lceil{m-d\over d+1}\rceil$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0809.1586 | |
| dc.identifier | http://arxiv.org/abs/0809.1586 | |
| dc.identifier | European J. Combin. 26 (2005) 617--627 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168738 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A20 | |
| dc.title | Proof of a conjecture on unimodality | |
| dc.type | text |