Incidence Theorems and Their Applications
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[1] David P. Woodruff. New Lower Bounds for General Locally Decodable Codes , 2007, Electron. Colloquium Comput. Complex..
[2] Alex Samorodnitsky,et al. A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents , 1998, STOC '98.
[3] Alex Iosevich,et al. Fourier analysis and geometric combinatorics , 2008 .
[4] Zeev Dvir,et al. Locally Decodable Codes with Two Queries and Polynomial Identity Testing for Depth 3 Circuits , 2007, SIAM J. Comput..
[5] Noga Alon,et al. Perturbed Identity Matrices Have High Rank: Proof and Applications , 2009, Combinatorics, Probability and Computing.
[6] Avi Wigderson,et al. Extractors: optimal up to constant factors , 2003, STOC '03.
[7] P. Erdös. On Sets of Distances of n Points , 1946 .
[8] U. Rothblum,et al. Scalings of matrices which have prespecified row sums and column sums via optimization , 1989 .
[9] Anthony J. W. Hilton,et al. On Double Diagonal and Cross Latin Squares , 1973 .
[10] Zeev Dvir,et al. On the size of Kakeya sets in finite fields , 2008, 0803.2336.
[11] József Beck,et al. On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry , 1983, Comb..
[12] Terence Tao,et al. A sum-product estimate in finite fields, and applications , 2003, math/0301343.
[13] Terence Tao,et al. BOUNDS ON ARITHMETIC PROJECTIONS, AND APPLICATIONS TO THE KAKEYA CONJECTURE , 1999 .
[14] Terence Tao,et al. Additive combinatorics , 2007, Cambridge studies in advanced mathematics.
[15] Terence Tao,et al. New bounds for Kakeya problems , 2001 .
[16] Ronald de Wolf,et al. Improved Lower Bounds for Locally Decodable Codes and Private Information Retrieval , 2004, ICALP.
[17] J. Tukey,et al. Generalized “sandwich” theorems , 1942 .
[18] Thomas Wolff,et al. Recent work connected with the Kakeya problem , 2007 .
[19] David E. Muller,et al. Application of Boolean algebra to switching circuit design and to error detection , 1954, Trans. I R E Prof. Group Electron. Comput..
[20] Avi Wigderson,et al. Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes , 2010, STOC '11.
[21] J. Kollár. Sharp effective Nullstellensatz , 1988 .
[22] Micha Sharir,et al. On the Number of Incidences Between Points and Curves , 1998, Combinatorics, Probability and Computing.
[23] Richard Sinkhorn. A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices , 1964 .
[24] Zeev Dvir,et al. Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits , 2005, STOC '05.
[25] L. M. Kelly,et al. A resolution of the sylvester-gallai problem of J.-P. serre , 1986, Discret. Comput. Geom..
[26] Avi Wigderson,et al. IMPROVED RANK BOUNDS FOR DESIGN MATRICES AND A NEW PROOF OF KELLY’S THEOREM , 2012, Forum of Mathematics, Sigma.
[27] Madhu Sudan,et al. Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers , 2013, SIAM J. Comput..
[28] J. Bourgain,et al. MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS , 2005 .
[29] Terence Tao,et al. From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE , 2000 .
[30] E. Szemerédi,et al. Crossing-Free Subgraphs , 1982 .
[31] Roy O. Davies,et al. Some remarks on the Kakeya problem , 1971, Mathematical Proceedings of the Cambridge Philosophical Society.
[32] Sergey Yekhanin,et al. Locally Decodable Codes , 2012, Found. Trends Theor. Comput. Sci..
[33] Larry Guth,et al. The endpoint case of the Bennett–Carbery–Tao multilinear Kakeya conjecture , 2008, 0811.2251.
[34] Avi Wigderson,et al. Kakeya Sets, New Mergers and Old Extractors , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.
[35] György Elekes,et al. On the number of sums and products , 1997 .
[36] Guy Kindler,et al. Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors , 2005, STOC '05.
[37] Endre Szemerédi,et al. A statistical theorem of set addition , 1994, Comb..
[38] Luca Trevisan,et al. Lower bounds for linear locally decodable codes and private information retrieval , 2006, computational complexity.
[39] Oliver Roche-Newton,et al. On an application of Guth-Katz theorem , 2011, 1103.1354.
[40] A. Besicovitch. On Kakeya's problem and a similar one , 1928 .
[41] Terence Tao,et al. Restriction and Kakeya phenomena for finite fields , 2002 .
[42] Haim Kaplan,et al. On lines, joints, and incidences in three dimensions , 2009, J. Comb. Theory, Ser. A.
[43] Endre Szemerédi,et al. Extremal problems in discrete geometry , 1983, Comb..
[44] Leonidas J. Guibas,et al. Counting and cutting cycles of lines and rods in space , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.
[45] Jonathan Katz,et al. On the efficiency of local decoding procedures for error-correcting codes , 2000, STOC '00.
[46] Oded Goldreich,et al. Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity , 1988, SIAM J. Comput..
[47] Zeev Dvir,et al. Tight Lower Bounds for 2-query LCCs over Finite Fields , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.
[48] Haim Kaplan,et al. Simple Proofs of Classical Theorems in Discrete Geometry via the Guth–Katz Polynomial Partitioning Technique , 2011, Discret. Comput. Geom..
[49] J. Matousek,et al. Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry , 2007 .
[50] Noam D. Elkies,et al. Sylvester–Gallai Theorems for Complex Numbers and Quaternions , 2004, Discret. Comput. Geom..
[51] Shubhangi Saraf,et al. Local List-Decoding and Testing of Random Linear Codes from High Error , 2013, SIAM J. Comput..
[52] Jean Bourgain,et al. On the Dimension of Kakeya Sets and Related Maximal Inequalities , 1999 .
[53] L. A S Z L,et al. Crossing Numbers and Hard Erdős Problems in Discrete Geometry , 1997 .
[54] Frank Thomson Leighton,et al. New lower bound techniques for VLSI , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).
[55] Jean Bourgain,et al. Multilinear Exponential Sums in Prime Fields Under Optimal Entropy Condition on the Sources , 2009 .
[56] Imre Bárány,et al. The convex hull of the integer points in a large ball , 1998 .
[57] Larry Guth,et al. On the Erdos distinct distance problem in the plane , 2010, 1011.4105.
[58] Leonidas J. Guibas,et al. Combinatorial complexity bounds for arrangements of curves and spheres , 1990, Discret. Comput. Geom..
[59] W. T. Gowers,et al. A New Proof of Szemerédi's Theorem for Arithmetic Progressions of Length Four , 1998 .
[60] Imre Z. Ruzsa. Sums of Finite Sets , 1996 .
[61] Melvyn B. Nathanson,et al. On sums and products of integers , 1997 .
[62] Irving S. Reed,et al. A class of multiple-error-correcting codes and the decoding scheme , 1954, Trans. IRE Prof. Group Inf. Theory.
[63] Madhu Sudan,et al. Improved lower bound on the size of Kakeya sets over finite fields , 2008, 0808.2499.
[64] Karol Borsuk. Drei Sätze über die n-dimensionale euklidische Sphäre , 1933 .
[65] Micha Sharir,et al. Incidences in three dimensions and distinct distances in the plane , 2010, Combinatorics, Probability and Computing.
[66] Endre Szemerédi,et al. On sums and products of integers , 1983 .
[67] Larry Guth,et al. Algebraic methods in discrete analogs of the Kakeya problem , 2008, 0812.1043.
[68] Haim Kaplan,et al. On Lines and Joints , 2009, Discret. Comput. Geom..
[69] Avi Wigderson,et al. Extracting Randomness Using Few Independent Sources , 2006, SIAM J. Comput..
[70] Avi Wigderson,et al. 2-source dispersers for sub-polynomial entropy and Ramsey graphs beating the Frankl-Wilson construction , 2006, STOC '06.