[seqfan] Re: R: Number of real roots of polynomial with coefficients +-1, or 0, +-1

israel at math.ubc.ca israel at math.ubc.ca
Sun Feb 26 20:02:41 CET 2017


Not sure what you mean by that.  E.g. x^5-x^4+x^3-x^2-x+1 has 3 real roots 
while x^5-x^4+x^3-x^2-x-1 has one. 

Cheers,
Robert

On Feb 26 2017, Luca Petrone wrote:

> I agree with Chai correction and extended by one term, so far. I noticed 
> that polynomials with c_0 and c_n of different sign have always same or 
> more nonzero real roots than polynomials with c_0 and c_n of same sign : 
> can this be demonstrated ? Best Regards, Luca Petrone
>
>> ----Messaggio originale---- Da: "Neil Sloane" <njasloane at gmail.com> 
>> Data: 26/02/2017 1.08 A: "Sequence Fanatics Discussion 
>> list"<seqfan at list.seqfan.eu> Ogg: [seqfan] Re Number of real roots of 
>> polynomial with coefficients +-1, or
>0, +-1
>>
>>OK, I added the third sequence to go along with A282691 and A282692: see
>>A282701. I guess this is probably what Oanh had in mind
>>when we started this discussion.  I put down a guess for the initial
>>entries, hoping that Chai Wah or Edwin or Luca will correct them if
>>necessary, and also extend them!
>>
>>Best regards
>>Neil
>>
>>Neil J. A. Sloane, President, OEIS Foundation.
>>11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>>Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>>Phone: 732 828 6098; home page: http://NeilSloane.com
>>Email: njasloane at gmail.com
>>
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