[seqfan] Re: Floretions, sufficient condition for conjecture
Creighton Kenneth Dement
creighton.k.dement at mail.uni-oldenburg.de
Sun Jun 28 12:14:27 CEST 2009
>> Dear Seqfans,
>>
>> I recently gave a list of five open conjectures.
>>
>> One of those conjectures is this one:
>>
>> X in Z^{infty} if and only if 4*tesseq(X) is a sequence of integers.
>
> Update: Of the five conjectures listed here
> http://www.scribd.com/doc/16091289/Conjectures?secret_password=87q0r68fbckohk6fms3
>
> conjectures 1 and 2 are now disproven. A counterexample is given at the
> link above (for me, it was hard to believe this example after a couple
> years of thinking otherwise).
>
> Conjecture 4 has been shown to be a result of conjecture 3 (the one at the
> top of this page). It is the content of corollaries 2.22/2.23 here:
> http://www.scribd.com/doc/14790151/Floretions-2009
Conjecture 3, though still a conjecture, has been entered as "Proposition
2.21" (page 18 of the above link) along as much of a proof as I could
muster (for months I've tried to form a proof using an entirely different
method. Yesterday, I basically threw it all away and started from
scratch). In this proof my question to the seqfan list is highlighted
purple. Alas, this is still related to the paragraph, below.
Sincerely,
Creighton
> So the big question left is whether conjecture 3 is valid. Note: I
> previously added this sentence to the conjecture "Assume forall m: X^m !=
> 0" in an attempt to avoid the trivial counterexample X = 1/8('i + 'jj').
> However, I forgot I mention in the introduction that the only fractional
> parts allowed for all base coefficients of X must be in the set {+-0.25,
> +-0.5, +- 0.75, 0}. Therefore, the counterexample does not apply.
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