%gmip.tex:
%Experimenting with the Garsia-Milne Involution Principle
%%a Plain TeX file by Shalosh B. Ekhad and Doron Zeilberger (x pages)

%begin macros
\def\L{{\cal L}}
\baselineskip=14pt
\parskip=10pt
\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\P{{\cal P}}
\def\Q{{\cal Q}}
\def\1{{\overline{1}}}
\def\2{{\overline{2}}}
\parindent=0pt
\overfullrule=0in
\def\Tilde{\char126\relax}
\def\frac#1#2{{#1 \over #2}}
%\headline={\rm  \ifodd\pageno  \RightHead  \else  \LeftHead  \fi}
%\def\RightHead{\centerline{
%Title
%}}
%\def\LeftHead{ \centerline{Doron Zeilberger}}
%end macros
\centerline
{\bf  
Experimenting with the Garsia-Milne Involution Principle
}
\bigskip
\centerline
{\it Shalosh B. EKHAD and Doron ZEILBERGER}

\bigskip

\qquad \qquad {\it In memory of Adriano M. Garsia (1928-2024) and in honor of Stephen C. Milne on his 75th birthday}


{\bf Abstract}: We use symbolic computation to find explicit expressions for the average, variance, and many higher moments, for the complexity of mappings produced by the amazing Garsia-Milne Involution Principle.

{\bf References}


[GM1] Adriano M. Garsia and Stephen C. Milne, {\it Method for constructing bijections for classical partition identities},
Proc. Nat. Acad. Sci. U.S.A.   {\bf 78} (1981), no. 4, 2026-2028.

[GM2] Adriano M. Garsia and Stephen C. Milne, {\it  A Rogers-Ramanujan bijection},
J. Combin. Theory Ser. A {\bf 31} (1981), no. 3, 289-339.

[S] Andrew V. Sills, {\it An invitation to the Rogers-Ramanujan identities}, CRC Press, 2018.

[Z] Doron Zeilberger, {\it Enumerative and Algebraic Combinatorics}, in:
``Princeton Companion to Mathematics'' , (Timothy Gowers, ed.), Princeton University Press,550-561, 2008.


\bigskip
\hrule
\bigskip
Shalosh B. Ekhad, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt ShaloshBEkhad at gmail  dot com}   \quad .
\bigskip
Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt DoronZeil at gmail  dot com}   \quad .

\bigskip

{\bf Jan. 25, 2025} 

\end

