
 
%begin macros 
\def\Tilde{\char126\relax}
\baselineskip=14pt
\parskip=10pt
\def\epsilon{\varepsilon}
\def\halmos{\hbox{\vrule height0.15cm width0.01cm\vbox{\hrule height
 0.01cm width0.2cm \vskip0.15cm \hrule height 0.01cm width0.2cm}\vrule
 height0.15cm width 0.01cm}}
\font\eightrm=cmr8 \font\sixrm=cmr6 
\font\eighttt=cmtt8
\magnification=\magstephalf
\def\lheading#1{\bigbreak \noindent {\bf#1} 
}
\parindent=0pt
\overfullrule=0in
\nopagenumbers
%end macros
\bigskip 
\centerline{\bf PROJECT SUMMARY}
\centerline{ \bf RIGOROUS EXPERIMENTAL COMBINATORICS} 
 
Doron Zeilberger proposes to continue to develop
methodologies for harnessing the great potential of
Computer Algebra to do research in Combinatorics and
related areas, and design experiments for (rigorous)
computer-assisted and computer-generated research.

In particular he hopes to develop a new, computer-assisted and
computer-generated phase, in the theory of permutation statistics;
explore seemingly intractable problems in combinatorial statistical
physics from the point of view of {\it symbolic}, rather than
{\it numeric}, computations; study lattice paths enumeration,
and extend the Wilf-Zeilberger algorithmic proof theory to
handle indefinitely many variables. He also hopes to tackle the
intriguing Razumov-Stroganov conjecture about so-called Fully
Packed Loops, that are in simple bijection with Alternating
Sign matrices.

This research should be symbiotic, as it is
expected that both the concrete results and 
the underlying methodologies, would help computer algebra developers
to improve and enhance their systems. It is also hoped that
this research will contribute to the budding field of Experimental
Mathematics, in that it will help develop a research methodology for
conducting computer experiments that output {\it rigorous} 
(and interesting!) mathematical theorems
(and proofs), rather than just verifying and formulating conjectures.

This research is in the field of Combinatorics, whose usefulness
to science and technology is well-known. In particular, computer
science is largely based on combinatorics, as is electronic
communication and the World Wide Web.



 

\end
