An Explicit Conjectured Determinant Evaluation Whose Proof
Would Make Me Happy (and the OEIS richer)
By Doron Zeilberger
.pdf
.ps
.tex
(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)
Written: Jan. 7, 2014
In my recent work on an interesting enumeration problem, I got "stuck". It all boils down
to proving a certain, seemingly simple, determinant evaluation. This
is a challenge for all you determinant-evaluation whizes, and an opportunity to make the OEIS
richer, since I am pledging 500 dollars for a proof and 50 dollars for a disproof
(in honor of the prover/disprover, with their name mentioned!)
Added Jan. 9, 2014: I posted this in the arxiv and got quite a few attempted proofs,
that unfortunately turned out to be wrong. Not surprisingly.
I `lied' when I said that "it came up in an enumeration problem". The conjectured
explicit determinant evaluation is a disguised form of "one half" of the notorious
Collatz problem, i.e. that there are no finite orbits. Congratulations to
those people who figured it out, including Robin Chapman, who kindly
permitted me to post his
proof of equivalence.
short Maple code.
Sample input and outpout
The
input file
produces the
output file
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