%AmandaKen.tex: 
%Frank Garvan's Counterexample to the Folsom-Ono  Andrews SPT Parity Theorem
%Can Be Discovered in Less Than 18 seconds
%%a Plain TeX file by Shalosh B. Ekhad

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\bf
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{
Frank Garvan's Counterexample to the Folsom-Ono  Andrews SPT Parity Theorem
}
\centerline
{
Can Be Discovered in Less Than 17 seconds
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\centerline{ {\it Shalosh B. EKHAD }\footnote{$^1$}
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c/o {\eighttt zeilberg  at math dot rutgers dot edu}.
\hfill \break
Exclusively published in: {\eighttt http://www.math.rutgers.edu/\~{}zeilberg/pj.html} .
Oct. 28, 2011.
}
}

Frank Garvan informed my master, Doron Zeilberger, that the statement of Theorem 1.2 in
[FO] is false as stated. A corrected version will appear in [AGL]. This got me curious
how long would it take me to discover this error, had I been asked to find it.
My master spent a few minutes writing a Maple code available from

{\eighttt http://www.math.rutgers.edu/\~{}zeilberg/tokhniot/CheckAmandaKen} .

Once copied into a Maple session, typing

{\tt CheckKenAmanda(507);}

returns (in $16.28$ seconds):

{\tt false} \quad .

(Note that $24 \cdot 507-1=23\cdot(23)^2$, but $spt(507)$ is even).

Furthermore, if the statement is already false, how can the
proof be correct? Alas, I have better things to do than try and fix their proof to fit
the corrected statement in [AGL], and besides what is the point? [AGL] give a brand new
proof that is much more appealing (at least to me) since it is {\it combinatorial} and
{\it elementary}, and does {\it not} use weak Maass forms and other fancy stuff.


{\bf References}

[AGL]  G.E. Andrews, F. G. Garvan, and J. Liang, {\it Self-conjugate vector partitions and the parity of
the spt-function}, in preparation.

[FO] A. Folsom and K. Ono, {\it The spt-function of Andrews}, Proc. Natl. Acad. Sci. USA {\bf 105} (2008), 20152-20156.






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