Created: Sept-Dec., 2003.

                           This version: Dec. 1, 2003

                  This is SMCper, a Maple package to implement

                  Doron Zeilberger's Symbolic Moment Calculus

                      applied to patterns in permutations

                       as it is described in his article

                  Symbolic Moment Calculus: I. Foundations and

                               Permutation-Patterns



             Written by Doron Zeilberger, zeilberg@math.rutgers.edu

``
                Please report bugs to zeilberg@math.rutgers.edu

``
              The most current version of this  package and paper

                               are  available from

                     http://www.math.rutgers.edu/~zeilberg/

         For a list of the MAIN procedures type ezra();, for help with

                a specific procedure, type ezra(procedure_name);



      For a list of the supporting procedures type ezra1();, for help with

          a specific supporting procedure, type ezra1(procedure_name);



Warning, the protected name Chi has been redefined and unprotected
[[{[3, 7, 1, 5, 4, 8, 2, 6], [3, 7, 1, 4, 5, 8, 2, 6]}, 1656661/
570004084241399808000000, .2906401982e-17], [{[3, 7, 4, 1, 8, 5, 2, 6], [5, 2,
8, 6, 3, 1, 7, 4]}, 4973119/1710012252724199424000000, .2908235887e-17], [{[3,
7, 1, 4, 8, 5, 2, 6], [3, 7, 1, 4, 6, 8, 2, 5]}, 332357/
114000816848279961600000, .2915391391e-17], [{[4, 7, 1, 3, 8, 5, 2, 6]}, 
5181929/1710012252724199424000000, .3030346123e-17], [{[3, 7, 1, 6, 4, 8, 2, 5]
, [3, 7, 1, 5, 8, 4, 2, 6]}, 38453/12666757427586662400000, .3035741406e-17], [
{[4, 7, 3, 1, 5, 8, 2, 6]}, 118229/38000272282759987200000, .3111267180e-17], [
{[3, 7, 5, 1, 8, 4, 2, 6], [5, 2, 8, 3, 6, 1, 7, 4]}, 44599/
14132332667142144000000, .3155813060e-17], [{[4, 7, 1, 3, 8, 6, 2, 5], [3, 7, 4
, 1, 8, 6, 2, 5]}, 5497699/1710012252724199424000000, .3215005618e-17], [{[3, 6
, 1, 8, 5, 2, 7, 4]}, 101041/31091131867712716800000, .3249833439e-17], [{[3, 6
, 2, 8, 5, 1, 7, 4], [3, 6, 8, 1, 4, 7, 2, 5]}, 514529/155455659338563584000000
, .3309811957e-17], [{[3, 7, 6, 1, 4, 8, 2, 5]}, 1907107/
570004084241399808000000, .3345777781e-17], [{[3, 7, 2, 5, 8, 4, 1, 6], [5, 2,
8, 4, 6, 1, 3, 7]}, 90169/26307880811141529600000, .3427452049e-17], [{[3, 6, 1
, 8, 4, 7, 2, 5], [3, 7, 1, 5, 8, 2, 6, 4]}, 5908543/1710012252724199424000000,
.3455263546e-17], [{[2, 6, 8, 4, 1, 5, 7, 3], [3, 7, 2, 6, 4, 8, 1, 5]}, 
1192987/342002450544839884800000, .3488241087e-17], [{[4, 7, 1, 5, 2, 8, 6, 3],
[3, 5, 8, 1, 4, 7, 2, 6]}, 5989897/1710012252724199424000000, .3502838644e-17],
[{[5, 2, 6, 8, 1, 3, 7, 4]}, 667991/190001361413799936000000, .3515716914e-17],
[{[2, 6, 4, 8, 1, 5, 7, 3], [5, 1, 8, 3, 6, 2, 7, 4]}, 2012849/
570004084241399808000000, .3531288732e-17], [{[3, 6, 1, 4, 8, 5, 2, 7], [3, 7,
1, 4, 6, 2, 8, 5]}, 6047143/1710012252724199424000000, .3536315597e-17], [{[3,
6, 8, 1, 5, 2, 7, 4], [3, 7, 2, 5, 8, 1, 6, 4]}, 1211999/
342002450544839884800000, .3543831332e-17], [{[2, 6, 3, 8, 5, 1, 7, 4], [3, 8,
6, 1, 4, 7, 2, 5]}, 469283/131539404055707648000000, .3567622975e-17], [{[3, 6,
1, 8, 4, 5, 2, 7], [3, 7, 1, 5, 6, 2, 8, 4]}, 556613/155455659338563584000000,
.3580525806e-17], [{[4, 7, 1, 5, 2, 8, 3, 6], [3, 5, 7, 1, 4, 8, 2, 6]}, 
6187717/1710012252724199424000000, .3618522025e-17], [{[6, 3, 2, 8, 5, 1, 7, 4]
}, 51151/14132332667142144000000, .3619430791e-17], [{[3, 7, 5, 2, 8, 4, 1, 6],
[2, 5, 8, 3, 6, 1, 7, 4]}, 1247167/342002450544839884800000, .3646661005e-17],
[{[3, 6, 1, 5, 8, 4, 2, 7], [3, 7, 1, 6, 4, 2, 8, 5]}, 6252943/
1710012252724199424000000, .3656665612e-17], [{[3, 6, 1, 8, 4, 2, 7, 5], [3, 6,
1, 5, 8, 2, 7, 4]}, 252547/68400490108967976960000, .3692181147e-17], [{[3, 6,
1, 8, 5, 4, 2, 7], [3, 7, 1, 6, 5, 2, 8, 4]}, 37447/10118415696592896000000, .\
3700875821e-17], [{[3, 6, 2, 8, 5, 1, 4, 7], [3, 6, 8, 2, 4, 7, 1, 5]}, 6366427
/1710012252724199424000000, .3723030048e-17], [{[3, 7, 4, 1, 8, 5, 6, 2], [5, 1
, 8, 6, 3, 2, 7, 4]}, 2130449/570004084241399808000000, .3737603043e-17], [{[3,
7, 2, 4, 6, 8, 1, 5], [3, 7, 4, 1, 5, 8, 6, 2]}, 255767/68400490108967976960000
, .3739256833e-17], [{[3, 6, 8, 1, 4, 5, 7, 2], [3, 7, 2, 6, 5, 1, 8, 4]}, 
1279451/342002450544839884800000, .3741057989e-17], [{[3, 7, 2, 4, 8, 5, 1, 6],
[5, 2, 8, 6, 4, 1, 3, 7]}, 1280977/342002450544839884800000, .3745519946e-17],
[{[4, 1, 8, 5, 3, 7, 2, 6], [2, 7, 5, 1, 4, 8, 6, 3]}, 23501/
6218226373542543360000, .3779373504e-17], [{[3, 6, 8, 1, 5, 4, 7, 2], [3, 7, 2,
5, 6, 1, 8, 4]}, 1294739/342002450544839884800000, .3785759423e-17], [{[4, 7, 3
, 1, 5, 8, 6, 2], [3, 7, 2, 4, 8, 6, 1, 5]}, 51943/13680098021793595392000, .\
3796975717e-17], [{[3, 7, 4, 2, 8, 5, 1, 6], [5, 2, 8, 6, 3, 1, 4, 7]}, 1300087
/342002450544839884800000, .3801396738e-17], [{[2, 6, 4, 8, 1, 5, 3, 7], [5, 1,
7, 3, 6, 2, 8, 4]}, 6525439/1710012252724199424000000, .3816018856e-17], [{[2,
7, 4, 1, 8, 5, 3, 6], [5, 2, 8, 6, 3, 7, 1, 4]}, 6528827/
1710012252724199424000000, .3818000128e-17], [{[3, 7, 4, 1, 6, 2, 8, 5], [2, 7,
4, 1, 6, 8, 3, 5]}, 2178749/570004084241399808000000, .3822339278e-17], [{[4, 7
, 2, 6, 1, 5, 8, 3], [2, 7, 5, 3, 8, 1, 6, 4]}, 198427/51818553112854528000000,
.3829265544e-17], [{[3, 6, 2, 8, 4, 1, 7, 5], [3, 6, 8, 4, 1, 7, 2, 5]}, 
6557359/1710012252724199424000000, .3834685389e-17], [{[3, 7, 4, 2, 6, 8, 1, 5]
, [3, 7, 4, 1, 6, 8, 5, 2]}, 1317839/342002450544839884800000, .3853302799e-17]
, [{[3, 7, 2, 5, 4, 8, 1, 6], [3, 7, 1, 5, 4, 8, 6, 2]}, 6590483/
1710012252724199424000000, .3854056010e-17], [{[3, 7, 6, 2, 4, 8, 1, 5], [3, 7,
6, 1, 4, 8, 5, 2]}, 1318819/342002450544839884800000, .3856168276e-17], [{[4, 7
, 1, 3, 8, 5, 6, 2], [4, 7, 2, 3, 8, 5, 1, 6]}, 6610867/
1710012252724199424000000, .3865976393e-17], [{[3, 6, 1, 7, 4, 2, 8, 5], [3, 6,
1, 5, 8, 2, 4, 7]}, 6621619/1710012252724199424000000, .3872264067e-17], [{[3,
7, 5, 1, 6, 2, 8, 4], [5, 3, 8, 1, 6, 4, 7, 2]}, 2207869/
570004084241399808000000, .3873426632e-17], [{[4, 7, 2, 6, 1, 8, 3, 5], [3, 7,
5, 1, 8, 2, 6, 4]}, 6647477/1710012252724199424000000, .3887385596e-17], [{[2,
6, 8, 4, 1, 7, 3, 5], [3, 6, 2, 8, 4, 7, 1, 5]}, 6651397/
1710012252724199424000000, .3889677977e-17], [{[4, 8, 5, 1, 3, 7, 2, 6], [2, 6,
8, 3, 1, 5, 7, 4]}, 1334051/342002450544839884800000, .3900705968e-17], [{[3, 7
, 4, 2, 8, 6, 1, 5], [2, 5, 8, 6, 1, 3, 7, 4]}, 121313/31091131867712716800000,
.3901852159e-17], [{[4, 7, 2, 3, 8, 6, 1, 5], [5, 2, 6, 8, 1, 4, 3, 7]}, 
2226559/570004084241399808000000, .3906215870e-17], [{[4, 7, 2, 5, 3, 8, 1, 6],
[3, 7, 1, 5, 8, 4, 6, 2]}, 6679943/1710012252724199424000000, .3906371425e-17],
[{[3, 6, 1, 8, 5, 2, 4, 7], [3, 6, 1, 7, 5, 2, 8, 4]}, 6697219/
1710012252724199424000000, .3916474276e-17], [{[3, 7, 5, 1, 8, 6, 2, 4], [5, 2,
6, 3, 8, 1, 7, 4]}, 611969/155455659338563584000000, .3936614483e-17], [{[3, 7,
1, 8, 4, 6, 2, 5], [3, 7, 1, 5, 8, 6, 2, 4]}, 448907/114000816848279961600000,
.3937752486e-17], [{[3, 6, 1, 4, 8, 7, 2, 5], [3, 7, 1, 4, 8, 2, 6, 5]}, 
6753163/1710012252724199424000000, .3949189831e-17], [{[4, 2, 8, 6, 5, 1, 7, 3]
, [3, 7, 1, 8, 4, 5, 2, 6]}, 450293/114000816848279961600000, .3949910294e-17],
[{[3, 7, 5, 2, 8, 6, 1, 4], [5, 2, 6, 3, 8, 1, 4, 7]}, 1355443/
342002450544839884800000, .3963255228e-17], [{[3, 7, 5, 1, 6, 8, 2, 4], [3, 7,
4, 6, 1, 8, 2, 5]}, 6777509/1710012252724199424000000, .3963427156e-17], [{[4,
7, 2, 6, 1, 8, 5, 3], [3, 7, 5, 2, 8, 1, 6, 4]}, 616337/
155455659338563584000000, .3964712527e-17], [{[6, 3, 7, 4, 1, 8, 5, 2], [4, 7,
1, 5, 2, 6, 8, 3], [3, 5, 8, 1, 4, 6, 2, 7], [4, 1, 7, 5, 2, 8, 6, 3]}, 6783067
/1710012252724199424000000, .3966677425e-17], [{[3, 5, 8, 1, 6, 4, 2, 7], [3, 8
, 5, 2, 6, 1, 7, 4]}, 755743/190001361413799936000000, .3977566236e-17], [{[2,
7, 3, 5, 8, 1, 6, 4], [3, 8, 6, 1, 5, 2, 7, 4]}, 1363283/
342002450544839884800000, .3986179040e-17], [{[3, 6, 8, 1, 4, 5, 2, 7], [3, 8,
2, 6, 5, 1, 7, 4]}, 524443/131539404055707648000000, .3986964999e-17], [{[3, 7,
1, 6, 8, 4, 2, 5]}, 1369429/342002450544839884800000, .4004149671e-17], [{[3, 7
, 2, 5, 8, 6, 1, 4], [5, 2, 6, 4, 8, 1, 3, 7]}, 24901/6218226373542543360000, .\
4004518090e-17], [{[2, 7, 5, 4, 8, 1, 6, 3], [3, 8, 1, 5, 6, 2, 7, 4]}, 1370003
/342002450544839884800000, .4005828022e-17], [{[3, 7, 4, 8, 1, 5, 2, 6], [5, 7,
1, 3, 6, 8, 2, 4]}, 6854719/1710012252724199424000000, .4008578880e-17], [{[2,
5, 8, 4, 1, 6, 3, 7], [3, 8, 6, 2, 4, 7, 1, 5]}, 2294179/
570004084241399808000000, .4024846599e-17], [{[3, 6, 8, 5, 1, 4, 7, 2], [3, 7,
2, 4, 6, 1, 8, 5]}, 106031/26307880811141529600000, .4030389250e-17], [{[3, 6,
2, 5, 8, 1, 7, 4], [3, 6, 8, 1, 5, 7, 2, 4]}, 6908479/1710012252724199424000000
, .4040017251e-17], [{[2, 5, 7, 4, 1, 8, 6, 3], [3, 6, 2, 7, 5, 1, 8, 4]}, 
6911167/1710012252724199424000000, .4041589169e-17], [{[3, 6, 1, 8, 5, 4, 7, 2]
, [3, 8, 1, 6, 5, 2, 7, 4]}, 1382939/342002450544839884800000, .4043652312e-17]
, [{[4, 7, 5, 1, 8, 3, 6, 2], [5, 1, 3, 8, 6, 2, 7, 4]}, 2305939/
570004084241399808000000, .4045478030e-17], [{[3, 5, 1, 8, 4, 7, 2, 6], [3, 7,
1, 5, 2, 8, 6, 4]}, 6926581/1710012252724199424000000, .4050603140e-17], [{[5,
1, 6, 3, 8, 2, 7, 4], [2, 6, 4, 8, 1, 3, 7, 5]}, 2309159/
570004084241399808000000, .4051127113e-17], [{[2, 7, 4, 1, 6, 3, 8, 5]}, 
6939671/1710012252724199424000000, .4058258056e-17], [{[3, 7, 2, 4, 5, 8, 1, 6]
, [3, 7, 1, 4, 5, 8, 6, 2]}, 6943283/1710012252724199424000000, .4060370321e-17
], [{[3, 5, 8, 2, 6, 1, 7, 4], [3, 5, 8, 1, 7, 4, 2, 6]}, 534397/
131539404055707648000000, .4062638141e-17], [{[3, 6, 5, 1, 8, 4, 2, 7], [5, 2,
8, 3, 6, 7, 1, 4]}, 632017/155455659338563584000000, .4065577302e-17], [{[3, 7,
1, 8, 5, 4, 2, 6], [3, 7, 1, 6, 5, 8, 2, 4]}, 4687/1151523402507878400000, .\
4070260309e-17], [{[3, 6, 4, 8, 1, 5, 7, 2], [5, 2, 7, 3, 6, 8, 1, 4]}, 535727/
131539404055707648000000, .4072749180e-17], [{[2, 5, 8, 4, 6, 1, 7, 3], [3, 7,
5, 2, 4, 8, 1, 6]}, 6967097/1710012252724199424000000, .4074296537e-17], [{[3,
7, 1, 4, 8, 5, 6, 2], [3, 8, 1, 4, 6, 7, 2, 5]}, 6968063/
1710012252724199424000000, .4074861446e-17], [{[3, 4, 7, 1, 5, 8, 2, 6], [3, 6,
1, 4, 7, 8, 2, 5]}, 6972697/1710012252724199424000000, .4077571368e-17], [{[3,
6, 2, 7, 4, 1, 8, 5], [3, 6, 8, 4, 1, 7, 5, 2]}, 6976687/
1710012252724199424000000, .4079904684e-17], [{[3, 5, 1, 7, 4, 8, 2, 6]}, 
6979963/1710012252724199424000000, .4081820460e-17], [{[3, 5, 8, 1, 6, 4, 7, 2]
, [3, 7, 5, 2, 6, 1, 8, 4]}, 2329529/570004084241399808000000, .4086863699e-17]
, [{[2, 6, 3, 8, 4, 1, 7, 5], [3, 8, 6, 4, 1, 7, 2, 5]}, 6998219/
1710012252724199424000000, .4092496407e-17], [{[6, 3, 2, 8, 5, 1, 4, 7], [3, 6,
7, 2, 4, 8, 1, 5]}, 7007263/1710012252724199424000000, .4097785258e-17], [{[4,
8, 5, 1, 6, 2, 7, 3], [5, 3, 1, 8, 6, 4, 2, 7]}, 42547/10363710622570905600000,
.4105382864e-17], [{[2, 7, 5, 1, 6, 3, 8, 4], [4, 1, 6, 8, 3, 5, 2, 7]}, 638821
/155455659338563584000000, .4109345409e-17], [{[4, 1, 8, 5, 6, 2, 7, 3], [3, 7,
5, 4, 1, 8, 6, 2]}, 56227/13680098021793595392000, .4110131368e-17], [{[4, 7, 3
, 2, 6, 8, 1, 5], [3, 7, 4, 1, 8, 6, 5, 2]}, 93791/22800163369655992320000, .\
4113610875e-17], [{[2, 7, 5, 4, 8, 1, 3, 6], [3, 8, 2, 5, 6, 1, 7, 4]}, 7035319
/1710012252724199424000000, .4114192158e-17], [{[3, 5, 7, 1, 8, 4, 2, 6], [5, 2
, 8, 3, 7, 1, 6, 4]}, 127949/31091131867712716800000, .4115289226e-17], [{[2, 6
, 4, 1, 8, 5, 3, 7], [4, 1, 7, 3, 6, 2, 8, 5]}, 7042879/
1710012252724199424000000, .4118613179e-17], [{[3, 8, 5, 2, 7, 4, 1, 6], [2, 5,
8, 3, 6, 1, 4, 7]}, 7047583/1710012252724199424000000, .4121364036e-17], [{[3,
5, 7, 1, 4, 8, 6, 2], [3, 6, 2, 7, 4, 8, 1, 5]}, 7051951/
1710012252724199424000000, .4123918404e-17], [{[3, 6, 2, 8, 5, 4, 1, 7], [5, 1,
7, 4, 3, 8, 6, 2]}, 7055227/1710012252724199424000000, .4125834180e-17], [{[3,
7, 5, 2, 6, 8, 1, 4], [3, 7, 4, 6, 1, 8, 5, 2]}, 108551/26307880811141529600000
, .4126178037e-17], [{[3, 7, 1, 4, 6, 8, 5, 2], [3, 7, 4, 2, 5, 8, 1, 6]}, 
7058237/1710012252724199424000000, .4127594401e-17], [{[2, 6, 8, 4, 1, 3, 7, 5]
, [3, 7, 2, 8, 4, 6, 1, 5]}, 1412227/342002450544839884800000, .4129289126e-17]
, [{[3, 6, 8, 1, 4, 2, 7, 5], [3, 7, 2, 8, 5, 1, 6, 4]}, 1413851/
342002450544839884800000, .4134037630e-17], [{[2, 7, 5, 3, 6, 1, 8, 4], [3, 8,
5, 1, 6, 4, 7, 2]}, 7096541/1710012252724199424000000, .4149994241e-17], [{[3,
7, 2, 5, 6, 8, 1, 4], [3, 7, 4, 5, 1, 8, 6, 2]}, 1420963/
342002450544839884800000, .4154832802e-17], [{[4, 8, 5, 1, 3, 7, 6, 2]}, 
7104983/1710012252724199424000000, .4154931047e-17], [{[3, 7, 6, 4, 1, 8, 2, 5]
, [3, 7, 6, 1, 5, 8, 2, 4]}, 2370367/570004084241399808000000, .4158508799e-17]
, [{[3, 5, 1, 8, 6, 4, 2, 7], [3, 7, 1, 6, 2, 5, 8, 4]}, 2370521/
570004084241399808000000, .4158778973e-17], [{[3, 5, 1, 8, 4, 6, 2, 7], [3, 7,
1, 5, 2, 6, 8, 4]}, 7119991/1710012252724199424000000, .4163707593e-17], [{[3,
7, 2, 8, 5, 4, 1, 6], [2, 6, 8, 3, 4, 1, 7, 5]}, 1427557/
342002450544839884800000, .4174113366e-17], [{[2, 7, 3, 6, 1, 5, 8, 4], [5, 1,
3, 8, 6, 4, 2, 7]}, 1428523/342002450544839884800000, .4176937907e-17], [{[3, 8
, 5, 1, 6, 4, 2, 7], [5, 2, 8, 3, 6, 4, 1, 7]}, 7144057/
1710012252724199424000000, .4177781176e-17], [{[3, 7, 4, 8, 1, 6, 2, 5], [5, 7,
1, 3, 8, 6, 2, 4]}, 7149979/1710012252724199424000000, .4181244309e-17], [{[2,
5, 8, 1, 4, 6, 7, 3], [3, 7, 6, 2, 5, 8, 1, 4]}, 1430371/
342002450544839884800000, .4182341377e-17], [{[4, 7, 1, 3, 8, 6, 5, 2], [3, 8,
4, 1, 7, 6, 2, 5]}, 11447/2736019604358719078400, .4183815051e-17], [{[3, 6, 1,
4, 8, 2, 7, 5]}, 1431659/342002450544839884800000, .4186107432e-17], [{[3, 7, 2
, 5, 1, 8, 6, 4]}, 7158967/1710012252724199424000000, .4186500412e-17], [{[2, 7
, 4, 1, 8, 6, 3, 5], [5, 2, 6, 8, 3, 7, 1, 4]}, 7160717/
1710012252724199424000000, .4187523796e-17], [{[3, 7, 6, 1, 5, 2, 8, 4], [2, 7,
6, 4, 1, 8, 3, 5]}, 1433423/342002450544839884800000, .4191265290e-17], [{[4, 7
, 2, 6, 1, 3, 8, 5], [2, 7, 5, 1, 8, 3, 6, 4]}, 7167521/
1710012252724199424000000, .4191502715e-17], [{[3, 7, 2, 6, 1, 4, 8, 5], [5, 3,
1, 6, 8, 4, 2, 7]}, 478657/114000816848279961600000, .4198715529e-17], [{[3, 6,
4, 8, 1, 5, 2, 7], [5, 1, 7, 3, 6, 8, 2, 4]}, 655537/155455659338563584000000,
.4216874463e-17], [{[2, 6, 4, 8, 3, 1, 7, 5], [4, 7, 2, 8, 3, 5, 1, 6]}, 
7220287/1710012252724199424000000, .4222359804e-17], [{[4, 2, 7, 6, 3, 1, 8, 5]
, [2, 6, 5, 1, 8, 4, 7, 3]}, 2412689/570004084241399808000000, .4232757390e-17]
, [{[3, 5, 8, 1, 4, 6, 7, 2], [3, 7, 6, 2, 5, 1, 8, 4]}, 7245151/
1710012252724199424000000, .4236900051e-17], [{[3, 6, 2, 8, 4, 5, 1, 7], [2, 6,
8, 4, 3, 7, 1, 5]}, 59887/14132332667142144000000, .4237587765e-17], [{[3, 8, 5
, 1, 4, 7, 6, 2], [5, 1, 8, 4, 6, 2, 3, 7]}, 2415461/570004084241399808000000,
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                      It took, 46.705, seconds of CPU time