[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.


> 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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