Connections in discrete mathematics: a celebration of the work of Ron Graham

367 Pages·2018·3.523 MB·English

by  Butler, Steve, Cooper, Joshua, Hurlbert, Glenn (eds.)

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
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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