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All pages | Previous page ("Low Dimensions" grant acknowledgments)
"Low Dimensions" grant acknowledgments"New Proof" grant acknowledgments3D Moser statistics
4D Moser brute force search4D Moser sets with d at least 2 have at most 42 points4D Moser sets with d at least 3 has at most 41 points
4D Moser sets with d at least 4 have at most 40 points4th roots of unity6th roots of unity
A-statistics codeABC conjecture
A Hilbert space lemmaA general partitioning principleA general result about density increments
A second Fourier decomposition related to Sperner's theoremA second outline of a density-increment argumentAbstract.tex
Abstract regularity lemmaAjtai-Szemerédi's proof of the corners theoremAlgebraic formulation of Hadwiger-Nelson problem
Algorithm for finding multiplicative sequences with bounded discrepancyAn efficient algorithm exists if Cramer's conjecture holds
An outline of a density-increment argumentAsymptotics of H tAustin's proof
Austin's proof IIBK:Section 3Basic facts about Bohr sets
Benchmarks of small admissible tuplesBertrand's postulateBiblio.tex
BibliographyBoshernitzan’s problemBounded Dirichlet inverse
Bounded discrepancy multiplicative functions do not correlate with charactersBounded gaps between primesBounding the derivative of H t
Bounding the derivative of H t - second approachBounding the derivative of H t - third approachBounding the discrepancy in terms of the common difference
C code for MoserCarlson's theoremCarlson-Simpson theorem
Character-like functionsClassification of (6,12,18,4,0) setsColoring.tex
Coloring Hales-Jewett theoremColoring R 2
Combinatorial subspaceComplexity of a set
Computer proof that completely multiplicative sequences have discrepancy greater than 2Computing a HAP basisConcentration of measure
Concepts.texControlling A+B/B 0Controlling H t-A-B/B 0
Convert raw input string into CSV tableCorners
Corners theoremCorrelation.texCorrelation with a 1-set implies correlation with a subspace
Cramer's conjectureCramer's random model for the primesCreate tables in an HTML file from an input sequence
DHJ(k) implies multidimensional DHJ(k)DJH(1,3)De Bruijn-Newman constant
Definable Banach SpacesDensity
Density increment method
Deolalikar P vs NP paper
Depth-first searchDepth-first search for multiplicative sequencesDhj-lown-lower.tex
Dhj.texDickson-Hardy-Littlewood theoremsDifferent upper and lower bound
Dirichlet inversesDiscrepancy 3 multiplicative sequence of length 13186Discrete logarithm
Discretized Borel Determinacy and P=NPDistribution of primes in smooth moduli
DriftDynamics of zerosEasy.tex
Effective bounds on H tEffective bounds on H t - second approachEqual-slices.tex
Equal-slices distribution for DHJ(k)Equal-slices measure
Ergodic-inspired methodsErgodic perspectiveEstimate the number of discrepancy 2 sequences
Estimating a sumExcluding bichromatic verticesExperimental results
FactoringFile outputFind a different parameter, show that it tends to infinity, and show that that implies that the discrepancy tends to infinity
Find a good configuration of HAPsFind set configurations that imply FUNCFinding narrow admissible tuples
Finding optimal k0 valuesFinding primesFinding primes with O(k) random bits
First obtain multiplicative structure and then obtain a contradictionFolkman's theoremForced Drift of Six in Multiplicative Sequences
Forced Drifts in Multiplicative SequencesFourier-analytic proof of SpernerFourier reduction
Frankl's union-closed conjectureFriedlander-Iwaniec theoremFujimura's problem
Fujimura.texFunction field versionFurstenberg-Katznelson argument
Furstenberg correspondence principleGeneralize to a graph-theoretic formulationGeneric prime
Genetic.texGenetic algorithm
Graham-Rothschild theoremHAP table for Sequence of length 1112HAP tables for Sequence of length 470
Hadwiger-Nelson problemHardy-Littlewood prime tuples conjecture
Higher-dimensional DHJ numbersHigher-dimensional FujimuraHigherk.tex
Hindman's theoremHorn clause formulationHuman proof of the 3D Pareto-optimal Moser statistics
Human proof that completely multiplicative sequences have discrepancy greater than 2Human proof that completely multiplicative sequences have discrepancy greater than 3
Hyper-optimistic conjectureIP-Szemerédi theoremImmerman's letter
Immerman-Vardi theoremImo 2009 q6Imo 2010
Imo 2011Imo 2012Improving the bounds for Roth's theorem
Influence of variablesInsensitive.texInteger.tex
Intransitive diceIntro.texIntroduction.tex
Iterated sumsets of log-primesJournal publishing reformJun Fukuyama's P≠NP Paper
Kakeya problemKolmogorov complexityKruskal-Katona theorem
Lattice approachLemma 1
Lemma 7Lemma 7.5Lemma 7.6
Lemma 8Length 1120 sequencesLength 1124 sequences
Limits with better propertiesLindell's CritiqueLine
Line-free sets correlate locally with complexity-1 setsLine free sets correlate locally with dense sets of complexity k-2
Linear normLinear norm grant acknowledgmentsList of results implied by the Riemann Hypothesis
LogoLongest constrained sequencesLookup table
Lookup table C codeLow discrepancy on PAPsLow discrepancy on primes and powers of 2
M=13 TheoremM=13 case of FUNCMain Page
Maple calculationsMatlab scriptMatryoshka Sequences
Maximal discrepancy-2 sequenceMeasures.texMeissel-Lehmer method
Modification of the Ajtai-Szemerédi argumentMoser's cube problem
Multiplicative.cMultiplicative sequencesNotes on polytope decomposition
Obstructions to uniformityObtaining the correct bound in Roth's discrepancy theoremOdlyzko's method
Omega(N)Online reactions to Deolalikar P vs NP paperOptimal a-set pair code
Optimal a-set pairsOracle counterexample to finding pseudoprimesOriginal Elsevier statement
Other proposed projectsOutline.texOutline of first paper
Outline of second paperOutro.texOverlapping Schwarz
P=NP implies a deterministic algorithm to find primesPartitioning.texPassing between measures
Polylog parameterizabilityPolymath.texPolymath1
Polymath15 grant acknowledgmentsPolymath15 test problem
Polymath4 grant acknowledgmentsPolymath8 grant acknowledgmentsPolynomial strategy
Prime counting functionPrime gapsProbabilistic formulation of Hadwiger-Nelson problem
Proof of DHJ(3) via density-incrementProposals for finding long low-discrepancy sequencesProve the result for shifted HAPs instead of HAPs
Pseudo-random generators (PRG)PseudointegersQuantum Arrow's Theorem
QuasirandomnessQue porra n tem nada pra fazer network penetration testRandom k-SAT
Refined greedy computation of multiplicative sequencesRepresentation of the diagonalRiemann-Siegel formula
Rota's conjectureRoth's Theorem concerning discrepancy on Arithmetic ProgressionRoth's theorem
Scanning codeSchinzel's hypothesis HSearch for completely multiplicative sequences
Second attempt at computing H t(x) for negative tSecond lookup table C code
Selberg sieve variational problemSequence of length 1091Sequence of length 1112
Sequence of length 3250Sequence of length 714Sequences given by modulated Sturmian functions
Shifts and signsShort sequences statisticsSide Proof 1
Side Proof 10Side Proof 2Side Proof 3
Side Proof 4Side Proof 5Side Proof 6
Side Proof 7Side Proof 8Side Proof 9
Signed sums of prime reciprocalsSlice
Smooth numberSperner's theorem
Sperner.texStability of eigenfunctionsStdout output
Stirling's formulaSylvester's sequenceSzemerédi's combinatorial proof of Roth's theorem
Szemerédi's original proof of Szemerédi's theoremSzemerédi's regularity lemmaSzemerédi's theorem
T2(x) = -T3(x)T2(x) = -x
T2(x) = T5(x) = -xT32-invariant sequencesT m(x) = (+/-)T n(x)
TeX files for first paperThe Erdos-Rado sunflower lemmaThe Erdős discrepancy problem
The HAP-subsequence structure of that sequenceThe complexity class BPPThe complexity class BQP
The complexity class DTIMEThe complexity class NPThe complexity class P
The complexity class promise-BPPThe cost of knowledgeThe first 1124-sequence
The hot spots conjectureThe polynomial Hirsch conjectureThe prime factors of the places where the first two sequences of length 1124 differ
Theproof.texThin trianglesThue-Morse-Hedlund Sequence
Tidy problem pageTimelineTimeline of prime gap bounds
Topological dynamics formulationTriangle removal lemmaUnsolved problems
UpdateUpdating partial sums with Fenwick treeUpper and lower bounds
Upper and lower discrepancyVectors for the dual SDPVerify the bounded discrepancy of an input sequence
Verify the bounded discrepancy of sequenceW-trickWirsing translation