studentim:= [MichaelDefreitas, BrianGarnett, EmilieHogan, DennisHou, JoshuaLoftus, KellenMyers, BrianNakamura, DanielaPrelipceanu, AsyaPritsker,ChristopherSadowski,AronSamkof,DavidWilson]: print(`Statistical Analysis of the Erdos, Zeilberger, and Shelah Numbers`): print(`Amongst the Audience in Doron Zeilberger's Erdos Memorial Lecture`): print(`Delievered 8:00-9:00PM, March 27, 2010`): print(``): print(`By Shalosh B. Ekhad`): print(`and students in Dr. Z.'s Spring 2010 Experimental Mathematics Class`): print(`consisting of the following`): print(studentim): Row1:=[ [RichardEhrenborg, 3, 3, 3], [PeterPery, 3, 4, 4], [TheodorosKyriopoulos, infinity, infinity, infinity]]: #Asya Pritsker Row2:= [[VeraPless, 2 , 3 , 3], [AndrewSchwartz, infinity , infinity , infinity], [DanDaly, 4, 5 , 4], [WaiYuenChan, 5, 5 , 5], [AlexEremenko, 2 , 4 , 3], [PavelBleher, 3 , 3 ,3 ], [AndyMartin, 4 , 5 , 4], [VirgilBarnard, infinity , infinity , infinity ]]: Row3:= [[MattMiller,4, 4, 4], [SaraBilley, 3, 3, 4], [AlexanderYong, 3, 3, 4], [DavidLeep, 3, 3, 3], [MarkMotley, infinity, infinity, infinity], [AlbertoCorso, 4, 4, 3], [BobDaverman, 4, 4, 3], [JayWood, 3,4,4] , [KatieMorrisa, infinity, infinity, infinity], [ManojKummini, 5, 6, 5], [LouizaFouli, 4, 5, 4], [LarsWChristensen, 4, 4, 4], [LianaSega, 4, 4, 4], [HenrikHolm, 5, 5, 5], [ShihweiChao, infinity, infinity, infinity], [BryceRichards, infinity, infinity, infinity]] : Row4:= [ [ MichaelSlone, 4, 4, 4 ], [ FernandoCamacho, 4, 6, 5 ], [ AlexanderSolynin, 2, 4, 3 ], [VladimirEiderman,2,4,3], [ VickiPowers, 2, 2, 3 ], [ JohnWermer, 3, 4, 3 ], [ BruceReznick, 1, 1, 2 ], [ WilliamHarris, infinity, infinity, infinity ], [ DougChatham, 3, 4, 4 ] ]: Row5:= [[JohnMackay,infinity,infinity,infinity], [MarieSnipes,4,5,5], [GwynBellamy,infinity,infinity,infinity], [DagMadsen,4,5,3], [MatjazKonvalinka,3,4,4], [ChiachiTung,infinity,infinity,infinity], [NickKirby,infinity,infinity,infinity], [BethKirby,infinity,infinity,infinity], [ElizabethWeaver,infinity,infinity,infinity], [DennisMoore,infinity,infinity,infinity], [AlexanderIzzo,4,5,4], [JenniferBiermann,infinity,infinity,infinity]]: Row6:=[ [PeterMiller,3,4,4], [RObertJenkins,infinity,infinity,infinity], [CatherineSulem,4,4,4], [JinhoBaik,3,4,4], [JustinDeVries,infinity,infinity,infinity], [MartinLorenz,3,3,3], [ClintonHines,infinity,infinity,infinity], [DanielWells,infinity,infinity,infinity], [TrieuLe,infinity,infinity,infinity], [AmilaAppuhamy,infinity,infinity,infinity], [EranNevo,2,3,3], [RichardFalk,4,4,4], [SergeiGelfand, 4, 3, 3], [MattMacauley, 4, 3, 5], [BryceRichards, infinity, infinity, infinity], [ShihweiChao, infinity, infinity, infinity] ]: #Brian N. Row7:= [[GaborHetyei,2,3,3], [PatriciaHersh,3,3,3], [WalterWhiteley,3,3,4], [SaulBlanco,2,3,3], [SethSullivant,3,4,4], [MeganOwen,3,4,4], [CarolineKlivans,3,3,4], [FelixEffenberger,4,4,4], [ThomasKahle,4,4,4], [MeiHuang, infinity, infinity, infinity], [RussWoodroofe,3,4,3], [SteveKlee,3,5,4], [BenjaminBraun,4,4,5], [JonathanBrowder,3,4,4]]: #End Brian N. Row8:= [[RobertCallihan,infinity,infinity, infinity], [AdamJackson,infinity,infinity, infinity], [MarshalLagani,infinity,infinity, infinity], [AlmutBurchard,3,4,4], [RichardLaugesen,3,3,4], [EvansHarrell,3,3,4], [GeorgeHagedorn,4,4, 4], [MarkAshbaugh,3,3, 4], [CatherineYan,2,2,2], [CarliniEnrico,3,4,4], [RobertoFontana,5,5, 5], [MikeMckenna,infinity,infinity,infinity]]: #EndEdi Row9:= [[MatthewZecknes,infinity,infinity,infinity], [EricClark, 4,4,4], [KelePonto,3,4,4], [JiyoonJung,infinity,infinity,infinity], [RobertHebble, infinity,infinity,infinity], [SaraElis, infinity,infinity,infinity], [JohnMoscoy,infinity,infinity,infinity], [JanTrlifaj,2,4,1], [MikeMays,1,3,2], [NathanielMays,infinity,infinity,infinity], [JeffreySchenker,4,4,4], [KaiCai, infinity,infinity,infinity], [MargieReaddy, 3, 4,4], [ThomasEhrenborg, infinity,infinity,infinity], [TheodoreEhrenborg, infinity,infinity,infinity]]: Row10:=[ [ArielBarton, infinity, infinity, infinity], [LuchezarAvramov, 3, 4, 4], [RobynLynnSnyder, infinity, infinity, infinity], [PeterMonk, 3, 3, 4], [SunilChebolu, 3, 4, 4], [DavidDrasin, 2, 4, 3], [PietroPoggiCorradini, 3, 4, 4], [KarelCasteels, 3, 4, 4], [KimRetert, 3, 5, 3], [SamuelKolins, 5, 7, 6], [RichardKlecker, infinity, infinity, infinity], [KurtLuoto, infinity, infinity, infinity], [AndyFrohmader, infinity, infinity, infinity] ]: Row11:=[ [DrewDuncan,infinity,infinity,infinity], [ThomasZaslavsky,2,3,3], [StephanieVanWilligenburg,3,3,4], [JohnMack,2,4,3], [KinHangChan,infinity,infinity,infinity], [HelgeKruger,4,4,4], [IrinaNenciu,4,5,5], [EllenKirkman,4,4,3], [SarahRaynor,4,4,4], [ErikStokes,infinity,infinity,infinity], [FabrizioZanello,4,4,4], [UweNagel,4,3,3], [JuanMigliore,3,3,4], [FebroRepello,infinity,infinity,infinity]]: EA:={op(Row1),op(Row2),op(Row3),op(Row4),op(Row5),op(Row6), op(Row7),op(Row8),op(Row9),op(Row10),op(Row11)}: EAin:={}: EAf:={}: for i in EA do if i[2]=infinity then EAin:= EAin union {i}: else EAf:= EAf union {i}: fi: od: EAin:={seq(EAin[i][1],i=1..nops(EAin))}: print(`There were`, nops(EA), `good and smart people` ): print(` who attended the 2010 Erdos Memorial Lecture`): print(`delivered by Doron Zeilberger `): print(`on March 27,2010, 8:00-9:00PM, at the 1057th American Mathematical`): print(`Society held at the Univesity of Kentucky, Lexington, KY, White Hall`): print(` Room 118 `): print(``): print(`Amongst them there were`, nops(EAin) , `people with an infinite `): print(` infinite Erdos number `): print(`Here they are `): print(EAin): print(`The remaining`, nops(EAf) , `people, together with their`): print(`Erdos, Zeilberger, and Shelah numbers were`): print(EAf): P:=add(x[i[1]]*E^i[2]*Z^i[3]*S^i[4],i in EAf): print(`The generating polynomial is`): print(P): print(`The largest Erdos number is`): print(degree(P,E)): print(`The largest Zeilberger number is`): print(degree(P,Z)): print(` (which is not so surprising since Zeilberger's Erdos number is 2)`): print(`The largest Shelah number is`): print(degree(P,S)): print(` (which is not so surprising since Shelah's Erdos number is 1)`): print(`The people with the largest Erdos Number (5) in the audience were`): P1:=coeff(P,E,5): print(P1): print(`The highest Zeilberger number among these is`): print(degree(P1,Z)): print(`and the people who have them`): P11:=coeff(P1,Z,7): print(P11): print(`Samuel Kolins is the lucky winner of the book`): print(`My Mind is open`): print(`In addition, I promised that book to a randomly chosen member`): print(`of the audience`): print(`Using Maple's random-number generator`): ra:=rand(1..129): print(`The lucky winner is`): print(EA[ra()]): print(`Now it is time for statistics`): print(`The generating function is`): Q:=add(E^i[2]*Z^i[3]*S^i[4],i in EAf): print(Q): QE:=subs({Z=1,S=1},Q): print(`The generating polynomial for Erdos Numbers is`): print(sort(QE)): QET:=subs(E=1,QE): print(`Out of the `, QET, `people in the audience with a finite`): print(`Erdos Number`): for i from 1 to degree(QE,E) do print(coeff(QE,E,i), `people have Erdos number`, i): print(`this is `, evalf(100*coeff(QE,E,i)/QET), `percent. `): od: ENmean:=subs(E=1,diff(QE,E))/QET: print(`The average Erdos number in the audience is`, evalf(ENmean)): print(`This is lower than the world average of`, 4.65 ): QE1:=QE/E^ENmean/QET: ENsd:=sqrt(subs(E=1,diff(E*diff(QE1,E),E))): print(`The standard deviation Erdos number in the audience is`, evalf(ENsd)): print(`This is lower than the world standard deviation of`, 1.21 ): QZ:=subs({E=1,S=1},Q): print(`The generating polynomial for Zeilberger Numbers is`): print(sort(QZ)): QZT:=subs(Z=1,QZ): print(`Out of the `, QZT, `people in the audience with a finite`): print(`Zeilberger Number`): for i from 1 to degree(QZ,Z) do print(coeff(QZ,Z,i), `people have Zeilberger number`, i): print(`this is `, evalf(100*coeff(QZ,Z,i)/QZT), `percent. `): od: ZNmean:=subs(Z=1,diff(QZ,Z))/QZT: print(`The average Zeilberger number in the audience is`, evalf(ZNmean)): QZ1:=QZ/Z^ZNmean/QZT: ZNsd:=sqrt(subs(Z=1,diff(Z*diff(QZ1,Z),Z))): print(`The standard deviation for the Zeilberger number in the audience is`, evalf(ZNsd)): QS:=subs({Z=1,E=1},Q): print(`The generating polynomial for Shelah Numbers is`): print(sort(QS)): QST:=subs(S=1,QS): print(`Out of the `, QST, `people in the audience with a finite`): print(`Shelah Number`): for i from 1 to degree(QS,S) do print(coeff(QS,S,i), `people have Shelah number`, i): print(`this is `, evalf(100*coeff(QS,S,i)/QST), `percent. `): od: SNmean:=subs(S=1,diff(QS,S))/QST: print(`The average Shelah number in the audience is`, evalf(SNmean)): QS1:=QS/S^SNmean/QST: SNsd:=sqrt(subs(S=1,diff(S*diff(QS1,S),S))): print(`The standard deviation for the Shelah number in the audience is`, evalf(SNsd)): Q1:=Q/E^ENmean/Z^ZNmean/S^SNmean/subs({E=1,S=1,Z=1},Q): print(`The centralized tri-variate generating function is`): print(Q1): c:=evalf(subs({E=1,Z=1,S=1},diff(diff(Q1,E),Z))/ENsd/ZNsd): print(`The correlation between the Erdos Number and the Zeilberger Number is`,c): c:=evalf(subs({E=1,Z=1,S=1},diff(diff(Q1,E),S))/ENsd/SNsd): print(`The correlation between the Erdos Number and the Shelah Number is`,c): c:=evalf(subs({E=1,Z=1,S=1},diff(diff(Q1,Z),S))/ZNsd/SNsd): print(`The correlation between the Zeilberger Number and the Shelah Number is`,c):