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"Low Dimensions" grant acknowledgments
"New Proof" grant acknowledgments
3D Moser statistics
4D Moser brute force search
4D Moser sets with d at least 2 have at most 42 points
4D Moser sets with d at least 3 has at most 41 points
4D Moser sets with d at least 4 have at most 40 points
4th roots of unity
6th roots of unity
6th unity roots
A-statistics code
ABC conjecture
A Hilbert space lemma
A general partitioning principle
A general result about density increments
A second Fourier decomposition related to Sperner's theorem
A second outline of a density-increment argument
Abstract.tex
Abstract regularity lemma
Ajtai-Szemerédi's proof of the corners theorem
Algebraic formulation of Hadwiger-Nelson problem
Algebraic line
Algorithm for finding multiplicative sequences with bounded discrepancy
An efficient algorithm exists if Cramer's conjecture holds
An outline of a density-increment argument
Asymptotics of H t
Austin's proof
Austin's proof II
BK:Section 3
Basic facts about Bohr sets
Benchmarks of small admissible tuples
Bertrand's postulate
Biblio.tex
Bibliography
Boshernitzan’s problem
Bounded Dirichlet inverse
Bounded discrepancy multiplicative functions do not correlate with characters
Bounded gaps between primes
Bounding the derivative of H t
Bounding the derivative of H t - second approach
Bounding the derivative of H t - third approach
Bounding the discrepancy in terms of the common difference
C code for Moser
Carlson's theorem
Carlson-Simpson theorem
Character-like functions
Classification of (6,12,18,4,0) sets
Coloring.tex
Coloring Hales-Jewett theorem
Coloring R 2
Combinatorial line
Combinatorial subspace
Complexity of a set
Computer proof that completely multiplicative sequences have at least 2
Computer proof that completely multiplicative sequences have discrepancy greater than 2
Computing a HAP basis
Concentration of measure
Concepts.tex
Controlling A+B/B 0
Controlling H t-A-B/B 0
Convert raw input string into CSV table
Corner
Corners
Corners theorem
Correlation.tex
Correlation with a 1-set implies correlation with a subspace
Cramer's conjecture
Cramer's random model for the primes
Create tables in an HTML file from an input sequence
DHJ
DHJ(1,3)
DHJ(2.5)
DHJ(2.6)
DHJ(2.7)
DHJ(3)
DHJ(k) implies multidimensional DHJ(k)
DJH(1,3)
De Bruijn-Newman constant
Definable Banach Spaces
Density
Density-increment methods
Density Hales-Jewett
Density Hales-Jewett theorem
Density increment method
Deolaikar's P!=NP paper
Deolalikar's P!=NP paper
Deolalikar P vs NP paper
Depth-first search
Depth-first search for multiplicative sequences
Dhj-lown-lower.tex
Dhj-lown.tex
Dhj.bib
Dhj.sty
Dhj.tex
Dickson-Hardy-Littlewood theorems
Different upper and lower bound
Dirichlet inverses
Discrepancy 3 multiplicative sequence of length 13186
Discrete logarithm
Discretized Borel Determinacy and P=NP
Distribution of primes in smooth moduli
Does Arrow's Theorem hold in quantum voting?
Drift
Dynamics of zeros
Easy.tex
Effective bounds on H t
Effective bounds on H t - second approach
Equal-slices.tex
Equal-slices density
Equal-slices distribution for DHJ(k)
Equal-slices measure
Ergodic-inspired methods
Ergodic perspective
Estimate the number of discrepancy 2 sequences
Estimating a sum
Excluding bichromatic vertices
Experimental results
Factoring
File output
Find 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 HAPs
Find set configurations that imply FUNC
Finding narrow admissible tuples
Finding optimal k0 values
Finding primes
Finding primes with O(k) random bits
First obtain multiplicative structure and then obtain a contradiction
Folkman's theorem
Forced Drift of Six in Multiplicative Sequences
Forced Drifts in Multiplicative Sequences
Fourier-analytic proof of Sperner
Fourier reduction
Frankl's union-closed conjecture
Friedlander-Iwaniec theorem
Fujimura's problem
Fujimura.tex
Function field version
Furstenberg-Katznelson argument
Furstenberg correspondence principle
Generalize to a graph-theoretic formulation
Generic prime
Genetic.tex
Genetic algorithm
Geometric line
Graham-Rothschild theorem
HAP table for Sequence of length 1112
HAP tables for Sequence of length 470
Hadwiger-Nelson problem
Hales-Jewett theorem
Hardy-Littlewood prime tuples conjecture
Higher-dimensional DHJ numbers
Higher-dimensional Fujimura
Higherk.tex
Hindman's theorem
Horn clause formulation
Human proof of the 3D Pareto-optimal Moser statistics
Human proof that completely multiplicative sequences have discrepancy at least 2
Human proof that completely multiplicative sequences have discrepancy greater than 2
Human proof that completely multiplicative sequences have discrepancy greater than 3
Hyper-optimistic conjecture
IP-Szemerédi theorem
Immerman's letter
Immerman-Vardi theorem
Imo 2009 q6
Imo 2010
Imo 2011
Imo 2012
Improving the bounds for Roth's theorem
Influence of variables
Insensitive.tex
Integer.tex
Intransitive dice
Intro.tex
Introduction.tex
Iterated sumsets of log-primes
Journal publishing reform
Jun Fukuyama's P≠NP Paper
Kakeya problem
Kolmogorov complexity
Kruskal-Katona theorem
LYM inequality
Lattice approach
Lemma 1
Lemma 7
Lemma 7.5
Lemma 7.6
Lemma 8
Length 1120 sequences
Length 1124 sequences
Limits with better properties
Lindell's Critique
Line
Line-free
Line-free sets correlate locally with complexity-1 sets
Line free sets correlate locally with dense sets of complexity k-2
Linear norm
Linear norm grant acknowledgments
List of results implied by the Riemann Hypothesis
Logo
Longest constrained sequences
Lookup table
Lookup table C code
Low discrepancy on PAPs
Low discrepancy on primes and powers of 2
M=13 Theorem
M=13 case of FUNC
Main Page
Maple calculations
Matlab script
Matryoshka Sequences
Maximal discrepancy-2 sequence
Measures.tex
Meissel-Lehmer method
Modification of the Ajtai-Szemerédi argument
Moser's cube problem
Moser's problem
Moser-lower.tex
Moser.tex
Moser set
Multiplicative.c
Multiplicative sequences
Notes on polytope decomposition
Obstructions to uniformity
Obtaining the correct bound in Roth's discrepancy theorem
Odlyzko's method
Omega(N)
Online reactions to Deolalikar P vs NP paper
Optimal a-set pair code
Optimal a-set pairs
Oracle counterexample to finding pseudoprimes
Original Elsevier statement
Other proposed projects
Outline.tex
Outline of first paper
Outline of second paper
Outro.tex
Overlapping Schwarz
P=NP implies a deterministic algorithm to find primes
Partitioning.tex
Passing between measures
Polylog parameterizability
Polymath.tex
Polymath1
Polymath14
Polymath15 test problem
Polymath4 grant acknowledgments
Polymath8 grant acknowledgments
Polynomial strategy
Prime counting function
Prime gaps
Probabilistic formulation of Hadwiger-Nelson problem
Proof of DHJ(3) via density-increment
Proposals for finding long low-discrepancy sequences
Prove the result for shifted HAPs instead of HAPs
Pseudo-random generators (PRG)
Pseudointegers
Quantum Arrow's Theorem
Quasirandomness
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Random k-SAT
Refined greedy computation of multiplicative sequences
Representation of the diagonal
Riemann-Siegel formula
Rota's conjecture
Roth's Theorem concerning discrepancy on Arithmetic Progression
Roth's theorem
Scanning code
Schinzel's hypothesis H
Search for completely multiplicative sequences
Second lookup table C code
Section 3: the "nd-estimate"
Selberg sieve variational problem
Sequence of length 1091
Sequence of length 1112
Sequence of length 3250
Sequence of length 714
Sequences given by modulated Sturmian functions
Shifts and signs
Short sequences statistics
Side Proof 1
Side Proof 10
Side Proof 2
Side Proof 3
Side Proof 4
Side Proof 5
Side Proof 6
Side Proof 7
Side Proof 8
Side Proof 9
Signed sums of prime reciprocals
Slice
Slices-equal
Slices-equal measure
Smooth number
Sperner's theorem
Sperner.tex
Stability of eigenfunctions
Stdout output
Stirling's formula
Sylvester's sequence
Szemerédi's combinatorial proof of Roth's theorem
Szemerédi's original proof of Szemerédi's theorem
Szemerédi's regularity lemma
Szemerédi's theorem
T2(x) = -T(x)
T2(x) = -T3(x)
T2(x) = -x
T2(x) = T5(x) = -x
T32-invariant sequences
T m(x) = (+/-)T n(x)
TeX files for first paper
The Erdos-Rado sunflower lemma
The Erdős discrepancy problem
The HAP-subsequence structure of that sequence
The complexity class BPP
The complexity class BQP
The complexity class DTIME
The complexity class NP
The complexity class P
The complexity class promise-BPP
The cost of knowledge
The first 1124-sequence
The hot spots conjecture
The polynomial Hirsch conjecture
The prime factors of the places where the first two sequences of length 1124 differ
Theproof.tex
Thin triangles
Thue-Morse-Hedlund Sequence
Tidy problem page
Timeline
Timeline of prime gap bounds
Topological dynamics formulation
Triangle removal lemma
Unsolved problems
Update
Updating partial sums with Fenwick tree
Upper and lower bounds
Upper and lower discrepancy
Vectors for the dual SDP
Verify the bounded discrepancy of an input sequence
Verify the bounded discrepancy of sequence
W-trick
Wirsing translation
Word algebra
Zero-free regions
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