%adr.tex: 
%Plain TeX
%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\W{{\cal W}}
\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

\bf
\centerline
{
The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r (between  1 and 30)
}
\rm
\bigskip
\centerline
{\it By Shalosh B. EKHAD and Doron ZEILBERGER}
\bigskip
\qquad \qquad \qquad \qquad \qquad \qquad 
{\it Dedicated to Ira Martin Gessel (b. April 9, 1951), on his millionth$_2$ birthday}
\bigskip

{\bf Preface: How many permutations are there of length googol+30 avoiding an increasing subsequence of length googol?}


This number is way too big for our physical universe, but the number of permutations 
of length googol+30 that {\it contains} at least one increasing subsequence of length googol is

$$
\displaylines{
3769987628815905643852921525646105664146833823621994801456991357113502936781270538054719048039675278 \cr
0769193354371721350001524610578097700045972792823897290959624203896101981952929640805170129282073883 \cr
4740018807571147534091229951249435913149171795302592312477456091277812321956212802204785578598020255 \cr
5625008802850838455586257402947256848380647181479993222566420025908679106917004348077812428261510240 \cr
6340176300585397517990032393036653951304924586489968650809789292291489270968710994809677050176596751 \cr
0725956202350750841376095024046396844968511243494784162014881795337835528626142808150073111101283361 \cr
0980701571937952824136796425017224636196853995950587943259043687431653922927840572864396105085190223}
$$
$$
\displaylines{
2582799067810378389890635196322425667467335158890500820128768331750855469963050322432973194472331947 \cr
0989825934469696079344723053679001130033667827524966034661782064851068214182454731365743413486729730 \cr
0631055444127725930013792836515384850702346797298406803049230145697433567004811555984158378611125895 \cr
0145768901348725550726037527669812626353266837685037397408862767082018239579392663024131792105407280 \cr
4788720840618514463465035392103884394981202007834724110094447116613439128758285044269471808502083275 \cr
6629374247928521501786839409853287740758570056230853738462527374534709641735458487560816949365616486 \cr
0695626913029699922648102091615529949414940648588048836485372758775808743231365617459515329190972398 \cr
7074543946415578728439994306071279654045146432379557541358408978156863172980419720839292761025261752 \cr
6805876626590163265795592248178664681630980893821587688413815206609216082514983787883386977226071420 \cr
21649147728993592578961422177700294482596740993986519357246959930668146505085270714475561150113747221 
}
$$

\end
