Connections in discrete mathematics: a celebration of the work of Ron Graham PDF
Preview Connections in discrete mathematics: a celebration of the work of Ron Graham
ConnectionsinDiscreteMathematics Discretemathematicshasbeenrisinginprominenceinthepastfiftyyears,bothasa toolwithpracticalapplicationsandasasourceofnewandinterestingmathematics. Thetopicsindiscretemathematicshavebecomesowelldevelopedthatitiseasyto forgetthatcommonthreadsconnectthedifferentareas,anditisthroughdiscovering andusingtheseconnectionsthatprogressisoftenmade. Formorethanfiftyyears,RonGrahamhasbeenabletoilluminatesomeofthese connectionsandhashelpedbringthefieldofdiscretemathematicstowhereitistoday. Tocelebratehiscontribution,thisvolumebringstogethermanyofthebestresearchers workingindiscretemathematics,includingFanChung,ErikDemaine,PersiDiaconis, PeterFrankl,AlHales,JeffreyLagarias,AllenKnutson,JanosPach,CarlPomerance, NeilSloane,andofcourseRonGrahamhimself. stevebutleristheBarbaraJJansonProfessorofMathematicsatIowaState University.Hisresearchinterestsincludespectralgraphtheory,enumerative combinatorics,mathematicsofjuggling,anddiscretegeometry.Heisthecoeditor ofTheMathematicsofPaulErdo˝s. joshuacooperisProfessorofMathematicsattheUniversityofSouthCarolina. HecurrentlyservesontheeditorialboardofInvolve.Hisresearchinterestsinclude spectralhypergraphtheory,linearandmultilinearalgebra,probabilisticcombinatorics, quasirandomness,combinatorialnumbertheory,andcomputationalcomplexity. glennhurlbertisProfessorandChairoftheDepartmentofMathematicsand AppliedMathematicsatVirginiaCommonwealthUniversity.Hisresearchinterests includeuniversalcycles,extremalsettheory,combinatorialoptimization, combinatorialbijections,andmathematicaleducation,andheisrecognizedasa leaderinthefieldofgraphpebbling. Connections in Discrete Mathematics A Celebration of the Work of Ron Graham Editedby STEVE BUTLER IowaStateUniversity JOSHUA COOPER UniversityofSouthCarolina GLENN HURLBERT VirginiaCommonwealthUniversity UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre, NewDelhi-110025,India 79AnsonRoad,#06-04/06,Singapore079906 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107153981 DOI:9781316650295 ©CambridgeUniversityPress2018 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2018 PrintedintheUnitedStatesofAmericabySheridanBooks,Inc. AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ISBN978-1-107-15398-1Hardback ISBN978-1-316-60788-6Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyInternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Contents ListofContributors pagevii Preface xi 1 ProbabilizingFibonacciNumbers 1 PersiDiaconis 2 OntheNumberofONCellsinCellularAutomata 13 N.J.A.Sloane 3 SearchforUltraflatPolynomialswithPlusandMinusOne Coefficients 39 AndrewOdlyzko 4 GeneralizedGoncˇarovPolynomials 56 RudolphLorentz,SalvatoreTringali,andCatherineH.Yan 5 TheDigraphDropPolynomial 86 FanChungandRonGraham 6 UnramifiedGraphCoversofFiniteDegree 104 Hau-WenHuangandWen-ChingWinnieLi 7 TheFirstFunctionandItsIterates 125 CarlPomerance 8 Erdo˝s,Klarner,andthe3x+1Problem 139 JeffreyC.Lagarias 9 AShortProofforanExtensionoftheErdo˝s–Ko–Rado Theorem 169 PeterFranklandAndreyKupavskii v vi Contents 10 TheHaight–RuzsaMethodforSetswithMoreDifferences thanMultipleSums 173 MelvynB.Nathanson 11 DimensionandCutVertices:AnApplicationofRamsey Theory 187 WilliamT.Trotter,BartoszWalczak,andRuidongWang 12 RecentResultsonPartitionRegularityofInfiniteMatrices 200 NeilHindman 13 SomeRemarksonπ 214 ChristianReiher,VojteˇchRödl,andMathiasSchacht 14 RamseyClasseswithClosureOperations(Selected CombinatorialApplications) 240 JanHubicˇkaandJaroslavNešetˇril 15 BorsukandRamseyTypeQuestionsinEuclideanSpace 259 PeterFrankl,JánosPach,ChristianReiher,andVojteˇchRödl 16 Pick’sTheoremandSumsofLatticePoints 278 KarlLevyandMelvynB.Nathanson 17 ApollonianRingPackings 283 AdrianBolt,SteveButler,andEspenHovland 18 JugglingandCardShufflingMeetMathematicalFonts 297 ErikD.DemaineandMartinL.Demaine 19 RandomlyJugglingBackwards 305 AllenKnutson 20 ExplicitErrorBoundsforLatticeEdgeworthExpansions 321 JoeP.Buhler,AnthonyC.Gamst,RonGraham,and AlfredW.Hales Contributors AdrianBolt IowaStateUniversity,Ames,IA50011,USA JoeP.Buhler CenterforCommunicationsResearch,SanDiego,CA92121,USA SteveButler IowaStateUniversity,Ames,IA50011,USA FanChung UniversityofCaliforniaatSanDiego,LaJolla,CA92093,USA ErikD.Demaine MITComputerScienceandArtificialIntelligenceLaboratory,Cambridge, MA02139,USA MartinL.Demaine MITComputerScienceandArtificialIntelligenceLaboratory,Cambridge, MA02139,USA PersiDiaconis DepartmentsofMathematicsandStatistics,StanfordUniversity,Stanford,CA 94305,USA PeterFrankl AlfrédRényiInstituteofMathematics,HungarianAcademyofSciences, H-1053Budapest,Hungary vii viii Contributors AnthonyC.Gamst CenterforCommunicationsResearch,SanDiego,CA92121,USA RonGraham UniversityofCaliforniaatSanDiego,LaJolla,CA92093,USA AlfredW.Hales CenterforCommunicationsResearch,SanDiego,CA92121,USA NeilHindman DepartmentofMathematics,HowardUniversity,Washington,DC20059, USA EspenHovland IowaStateUniversity,Ames,IA50011,USA Hau-WenHuang DepartmentofMathematics,NationalCentralUniversity,Chung-Li32001, Taiwan JanHubicˇka ComputerScienceInstituteofCharlesUniversity(IUUK),CharlesUniversity, 11800Praha,CzechRepublic AllenKnutson CornellUniversity,Ithaca,NY14853,USA AndreyKupavskii MoscowInstituteofPhysicsandTechnology,Dolgobrudny,MoscowRegion, 141701,RussianFederation;andUniversityofBirmingham,Birmingham, B152TT,UK JeffreyC.Lagarias DepartmentofMathematics,UniversityofMichigan,AnnArbor,MI 48109–1043,USA KarlLevy DepartmentofMathematics,BoroughofManhattanCommunityCollege (CUNY),NewYork,NY10007,USA Contributors ix Wen-ChingWinnieLi DepartmentofMathematics,PennsylvaniaStateUniversity,UniversityPark, PA16802,USA RudolphLorentz ScienceProgram,TexasA&MUniversityatQatar,Doha,Qatar MelvynB.Nathanson DepartmentofMathematics,LehmanCollege(CUNY),Bronx,NY10468, USA JaroslavNešetrˇil ComputerScienceInstituteofCharlesUniversity(IUUK),CharlesUniversity, 11800Praha,CzechRepublic AndrewOdlyzko SchoolofMathematics,UniversityofMinnesota,Minneapolis,MN55455, USA JánosPach RényiInstituteandEPFL,Station8,CH-1014Lausanne,Switzerland CarlPomerance MathematicsDepartment,DartmouthCollege,Hanover,NH03755,USA ChristianReiher FachbereichMathematik,UniversitätHamburg,20146Hamburg,Germany VojteˇchRödl DepartmentofMathematicsandComputerScience,EmoryUniversity, Atlanta,GA30322,USA MathiasSchacht FachbereichMathematik,UniversitätHamburg,20146Hamburg,Germany N.J.A.Sloane TheOEISFoundationInc.,11SouthAdelaideAve.,HighlandPark,NJ 08904,USA
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