Statistical Analysis of the Erdos, Zeilberger, and Shelah Numbers Amongst the Audience in Doron Zeilberger's Erdos Memorial Lecture Delievered 8:00-9:00PM, March 27, 2010 By Shalosh B. Ekhad and students in Dr. Z.'s Spring 2010 Experimental Mathematics Class consisting of the following [MichaelDefreitas, BrianGarnett, EmilieHogan, DennisHou, JoshuaLoftus, KellenMyers, BrianNakamura, DanielaPrelipceanu, AsyaPritsker, ChristopherSadowski, AronSamkof, DavidWilson] -------------------------------------------------------------------------- There were, 130, good and smart people who attended the 2010 Erdos Memorial Lecture delivered by Doron Zeilberger on March 27,2010, 8:00-9:00PM, at the 1057th American Mathematical Society held at the Univesity of Kentucky, Lexington, KY, White Hall Room 118 Amongst them there were, 44, people with an infinite Erdos number Here they are {NathanielMays, KaiCai, TrieuLe, AdamJackson, ArielBarton, BethKirby, ChiachiTung, DanielWells, DennisMoore, DrewDuncan, ErikStokes, GwynBellamy, JiyoonJung, JohnMackay, JohnMoscoy, KinHangChan, KurtLuoto, MarkMotley, MeiHuang, MikeMckenna, NickKirby, SaraElis, ShihweiChao, AmilaAppuhamy, AndrewSchwartz, AndyFrohmader, BryceRichards, ClintonHines, ElizabethWeaver, FebroRepello, JustinDeVries, KatieMorrisa, MarshalLagani, MatthewZecknes, RObertJenkins, RichardKlecker, RobertCallihan, RobertHebble, RobynLynnSnyder, ThomasEhrenborg, VirgilBarnard, WilliamHarris, JenniferBiermann, TheodoreEhrenborg, TheodorosKyriopoulos} The remaining, 85, people, together with their Erdos, Zeilberger, and Shelah numbers were {[DanDaly, 4, 5, 4], [JayWood, 3, 4, 4], [AndyMartin, 4, 5, 4], [BobDaverman, 4, 4, 3], [DagMadsen, 4, 5, 3], [DavidDrasin, 2, 4, 3], [DavidLeep, 3, 3, 3], [DougChatham, 3, 4, 4], [EranNevo, 2, 3, 3], [EricClark, 4, 4, 4], [GaborHetyei, 2, 3, 3], [HelgeKruger, 4, 4, 4], [HenrikHolm, 5, 5, 5], [IrinaNenciu, 4, 5, 5], [JanTrlifaj, 2, 4, 1], [JinhoBaik, 3, 4, 4], [JohnMack, 2, 4, 3], [JohnWermer, 3, 4, 3], [KelePonto, 3, 4, 4], [KimRetert, 3, 5, 3], [LianaSega, 4, 4, 4], [LouizaFouli, 4, 5, 4], [MarieSnipes, 4, 5, 5], [MattMiller, 4, 4, 4], [MeganOwen, 3, 4, 4], [MikeMays, 1, 3, 2], [PavelBleher, 3, 3, 3], [PeterMiller, 3, 4, 4], [PeterMonk, 3, 3, 4], [PeterPery, 3, 4, 4], [RichardFalk, 4, 4, 4], [SaraBilley, 3, 3, 4], [SarahRaynor, 4, 4, 4], [SaulBlanco, 2, 3, 3], [SteveKlee, 3, 5, 4], [ThomasKahle, 4, 4, 4], [UweNagel, 4, 3, 3], [VeraPless, 2, 3, 3], [VickiPowers, 2, 2, 3], [WaiYuenChan, 5, 5, 5], [AlbertoCorso, 4, 4, 3], [AlexEremenko, 2, 4, 3], [AlexanderIzzo, 4, 5, 4], [AlexanderYong, 3, 3, 4], [AlmutBurchard, 3, 4, 4], [BenjaminBraun, 4, 4, 5], [BruceReznick, 1, 1, 2], [CarliniEnrico, 3, 4, 4], [CarolineKlivans, 3, 3, 4], [CatherineSulem, 4, 4, 4], [CatherineYan, 2, 2, 2], [EllenKirkman, 4, 4, 3], [EvansHarrell, 3, 3, 4], [FabrizioZanello, 4, 4, 4], [FernandoCamacho, 4, 6, 5], [GeorgeHagedorn, 4, 4, 4], [JeffreySchenker, 4, 4, 4], [JonathanBrowder, 3, 4, 4], [JuanMigliore, 3, 3, 4], [KarelCasteels, 3, 4, 4], [LuchezarAvramov, 3, 4, 4], [ManojKummini, 5, 6, 5], [MargieReaddy, 3, 4, 4], [MarkAshbaugh, 3, 3, 4], [MartinLorenz, 3, 3, 3], [MattMacauley, 4, 3, 5], [MichaelSlone, 4, 4, 4], [PatriciaHersh, 3, 3, 3], [RichardLaugesen, 3, 3, 4], [RobertoFontana, 5, 5, 5], [RussWoodroofe, 3, 4, 3], [SamuelKolins, 5, 7, 6], [SergeiGelfand, 4, 3, 3], [SethSullivant, 3, 4, 4], [SunilChebolu, 3, 4, 4], [ThomasZaslavsky, 2, 3, 3], [WalterWhiteley, 3, 3, 4], [AlexanderSolynin, 2, 4, 3], [FelixEffenberger, 4, 4, 4], [LarsWChristensen, 4, 4, 4], [MatjazKonvalinka, 3, 4, 4], [RichardEhrenborg, 3, 3, 3], [VladimirEiderman, 2, 4, 3], [PietroPoggiCorradini, 3, 4, 4], [StephanieVanWilligenburg, 3, 3, 4]} The generating polynomial is 4 5 4 3 4 4 4 5 4 x[DanDaly] E Z S + x[JayWood] E Z S + x[AndyMartin] E Z S 4 4 3 4 5 3 + x[BobDaverman] E Z S + x[DagMadsen] E Z S 2 4 3 3 3 3 + x[DavidDrasin] E Z S + x[DavidLeep] E Z S 3 4 4 2 3 3 4 4 4 + x[DougChatham] E Z S + x[EranNevo] E Z S + x[EricClark] E Z S 2 3 3 4 4 4 + x[GaborHetyei] E Z S + x[HelgeKruger] E Z S 5 5 5 4 5 5 2 4 + x[HenrikHolm] E Z S + x[IrinaNenciu] E Z S + x[JanTrlifaj] E Z S 3 4 4 2 4 3 3 4 3 + x[JinhoBaik] E Z S + x[JohnMack] E Z S + x[JohnWermer] E Z S 3 4 4 3 5 3 4 4 4 + x[KelePonto] E Z S + x[KimRetert] E Z S + x[LianaSega] E Z S 4 5 4 4 5 5 + x[LouizaFouli] E Z S + x[MarieSnipes] E Z S 4 4 4 3 4 4 3 2 + x[MattMiller] E Z S + x[MeganOwen] E Z S + x[MikeMays] E Z S 3 3 3 3 4 4 + x[PavelBleher] E Z S + x[PeterMiller] E Z S 3 3 4 3 4 4 4 4 4 + x[PeterMonk] E Z S + x[PeterPery] E Z S + x[RichardFalk] E Z S 3 3 4 4 4 4 + x[SaraBilley] E Z S + x[SarahRaynor] E Z S 2 3 3 3 5 4 4 4 4 + x[SaulBlanco] E Z S + x[SteveKlee] E Z S + x[ThomasKahle] E Z S 4 3 3 2 3 3 2 2 3 + x[UweNagel] E Z S + x[VeraPless] E Z S + x[VickiPowers] E Z S 5 5 5 4 4 3 + x[WaiYuenChan] E Z S + x[AlbertoCorso] E Z S 2 4 3 4 5 4 + x[AlexEremenko] E Z S + x[AlexanderIzzo] E Z S 3 3 4 3 4 4 + x[AlexanderYong] E Z S + x[AlmutBurchard] E Z S 4 4 5 2 + x[BenjaminBraun] E Z S + x[BruceReznick] E Z S 3 4 4 3 3 4 + x[CarliniEnrico] E Z S + x[CarolineKlivans] E Z S 4 4 4 2 2 2 + x[CatherineSulem] E Z S + x[CatherineYan] E Z S 4 4 3 3 3 4 + x[EllenKirkman] E Z S + x[EvansHarrell] E Z S 4 4 4 4 6 5 + x[FabrizioZanello] E Z S + x[FernandoCamacho] E Z S 4 4 4 4 4 4 + x[GeorgeHagedorn] E Z S + x[JeffreySchenker] E Z S 3 4 4 3 3 4 + x[JonathanBrowder] E Z S + x[JuanMigliore] E Z S 3 4 4 3 4 4 + x[KarelCasteels] E Z S + x[LuchezarAvramov] E Z S 5 6 5 3 4 4 + x[ManojKummini] E Z S + x[MargieReaddy] E Z S 3 3 4 3 3 3 + x[MarkAshbaugh] E Z S + x[MartinLorenz] E Z S 4 3 5 4 4 4 + x[MattMacauley] E Z S + x[MichaelSlone] E Z S 3 3 3 3 3 4 + x[PatriciaHersh] E Z S + x[RichardLaugesen] E Z S 5 5 5 3 4 3 + x[RobertoFontana] E Z S + x[RussWoodroofe] E Z S 5 7 6 4 3 3 + x[SamuelKolins] E Z S + x[SergeiGelfand] E Z S 3 4 4 3 4 4 + x[SethSullivant] E Z S + x[SunilChebolu] E Z S 2 3 3 3 3 4 + x[ThomasZaslavsky] E Z S + x[WalterWhiteley] E Z S 2 4 3 4 4 4 + x[AlexanderSolynin] E Z S + x[FelixEffenberger] E Z S 4 4 4 3 4 4 + x[LarsWChristensen] E Z S + x[MatjazKonvalinka] E Z S 3 3 3 2 4 3 + x[RichardEhrenborg] E Z S + x[VladimirEiderman] E Z S 3 4 4 3 3 4 + x[PietroPoggiCorradini] E Z S + x[StephanieVanWilligenburg] E Z S The largest Erdos number is 5 The largest Zeilberger number is 7 (which is not so surprising since Zeilberger's Erdos number is 2) The largest Shelah number is 6 (which is not so surprising since Shelah's Erdos number is 1) The people with the largest Erdos Number (5) in the audience were 5 5 5 5 6 5 x[HenrikHolm] Z S + x[WaiYuenChan] Z S + x[ManojKummini] Z S 5 5 7 6 + x[RobertoFontana] Z S + x[SamuelKolins] Z S The highest Zeilberger number among these is 7 and the people who have them 6 x[SamuelKolins] S Samuel Kolins is the lucky winner of the book My Mind is open In addition, I promised that book to a randomly chosen member of the audience Using Maple's random-number generator The lucky winner is [ManojKummini, 5, 6, 5] Now it is time for statistics The generating function is 3 2 4 4 5 2 2 2 2 4 6 5 5 6 5 4 3 5 E Z S + E Z S + E Z S + E Z S + E Z S + E Z S + E Z S 5 7 6 2 4 3 2 4 3 3 3 4 5 5 5 5 5 + E Z S + 5 E Z S + E Z S + 5 E Z S + 2 E Z S + 3 E Z S 3 4 3 3 5 3 4 5 3 2 3 3 4 4 4 + 2 E Z S + E Z S + E Z S + 5 E Z S + 14 E Z S 3 4 4 4 5 4 4 4 3 3 3 4 3 5 4 + 17 E Z S + 4 E Z S + 3 E Z S + 10 E Z S + E Z S 4 3 3 2 2 3 + 2 E Z S + E Z S The generating polynomial for Erdos Numbers is 5 4 3 2 5 E + 29 E + 36 E + 13 E + 2 E Out of the , 85, people in the audience with a finite Erdos Number 2, people have Erdos number, 1 this is , 2.352941176, percent. 13, people have Erdos number, 2 this is , 15.29411765, percent. 36, people have Erdos number, 3 this is , 42.35294118, percent. 29, people have Erdos number, 4 this is , 34.11764706, percent. 5, people have Erdos number, 5 this is , 5.882352941, percent. The average Erdos number in the audience is, 3.258823529 This is lower than the world average of, 4.65 The standard deviation Erdos number in the audience is, 0.8697929594 This is lower than the world standard deviation of, 1.21 The generating polynomial for Zeilberger Numbers is 7 6 5 4 3 2 Z + 2 Z + 12 Z + 43 Z + 24 Z + 2 Z + Z Out of the , 85, people in the audience with a finite Zeilberger Number 1, people have Zeilberger number, 1 this is , 1.176470588, percent. 2, people have Zeilberger number, 2 this is , 2.352941176, percent. 24, people have Zeilberger number, 3 this is , 28.23529412, percent. 43, people have Zeilberger number, 4 this is , 50.58823529, percent. 12, people have Zeilberger number, 5 this is , 14.11764706, percent. 2, people have Zeilberger number, 6 this is , 2.352941176, percent. 1, people have Zeilberger number, 7 this is , 1.176470588, percent. The average Zeilberger number in the audience is, 3.858823529 The standard deviation for the Zeilberger number in the audience is, 0.8964366211 The generating polynomial for Shelah Numbers is 6 5 4 3 2 S + 9 S + 46 S + 25 S + 3 S + S Out of the , 85, people in the audience with a finite Shelah Number 1, people have Shelah number, 1 this is , 1.176470588, percent. 3, people have Shelah number, 2 this is , 3.529411765, percent. 25, people have Shelah number, 3 this is , 29.41176471, percent. 46, people have Shelah number, 4 this is , 54.11764706, percent. 9, people have Shelah number, 5 this is , 10.58823529, percent. 1, people have Shelah number, 6 this is , 1.176470588, percent. The average Shelah number in the audience is, 3.729411765 The standard deviation for the Shelah number in the audience is, 0.7879718610 The centralized tri-variate generating function is 3 2 4 4 5 2 2 2 2 4 6 5 5 6 5 4 3 5 (E Z S + E Z S + E Z S + E Z S + E Z S + E Z S + E Z S 5 7 6 2 4 3 2 4 3 3 3 4 5 5 5 5 5 + E Z S + 5 E Z S + E Z S + 5 E Z S + 2 E Z S + 3 E Z S 3 4 3 3 5 3 4 5 3 2 3 3 4 4 4 + 2 E Z S + E Z S + E Z S + 5 E Z S + 14 E Z S 3 4 4 4 5 4 4 4 3 3 3 4 3 5 4 + 17 E Z S + 4 E Z S + 3 E Z S + 10 E Z S + E Z S / 277 328 317\ | --- --- ---| 4 3 3 2 2 3 / | 85 85 85 | + 2 E Z S + E Z S ) / \85 E Z S / / The correlation between the Erdos Number and the Zeilberger Number is, 0.6353139173 The correlation between the Erdos Number and the Shelah Number is, 0.7029745058 The correlation between the Zeilberger Number and the Shelah Number is, 0.5788184166