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

Luca Petrone luca.petrone at libero.it
Sun Feb 26 23:05:44 CET 2017


I was meaning that, for a given n, the max number of nonzero real roots  with 
c_0 and c_n of different sign is always >= the  max number of nonzero real 
roots  with c_0 and c_n of same sign. E.g., for n=6, they are 4 and 2, 
respectively.
Bye, Luca


>----Messaggio originale----
>Da: israel at math.ubc.ca
>Data: 26/02/2017 20.02
>A: "Sequence Fanatics Discussion list"<seqfan at list.seqfan.eu>
>Ogg: [seqfan] Re: R: Number of real roots of polynomial with coefficients +-
1, or 0, +-1
>
>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
>>>
>>>--
>>>Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>
>>
>>
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>
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