Long arithmetic progressions in sumsets: Thresholds and bounds

Endre Szemerédi, Van Vu

Type: Article

Publication Date: 2005-09-13

Citations: 47

DOI: https://doi.org/10.1090/s0894-0347-05-00502-3

View Publication

Locations

Journal of the American Mathematical Society - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	The distribution of smooth numbers in arithmetic progressions	1992	Antal Balog Carl Pomerance
+	Long arithmetic progressions in sumsets: Thresholds and Bounds	2005	Endre Szemerédi Van Vu
+ PDF Chat	The structure of higher sumsets	2022	Vsevolod F. Lev
+	Signed sums of terms of a sequence	2012	Fengjuan Chen Yong-Gao Chen
+ PDF Chat	𝑑-complete sequences of integers	1996	Péter L. Erdős Mordechai Lewin
+ PDF Chat	Arithmetic progressions consisting only of primes	1979	Emil Grosswald Peter Hagis
+	Integer Sum Sets Containing Long Arithmetic Progressions	1992	Gregory A. Freiman H. Halberstam Imre Z. Ruzsa
+ PDF Chat	Sets of integers with nonlong arithmetic progressions generated by the greedy algorithm	1979	Joseph L. Gerver L. Thomas Ramsey
+ PDF Chat	On 𝑘-free sequences of integers	1972	Samuel S. Wagstaff
+ PDF Chat	On sequences not containing a large sum-free subsequence	1973	S. L. G. Choi
+ PDF Chat	The sum of the reciprocals of a set of integers with no arithmetic progression of 𝑘 terms	1977	Joseph L. Gerver
+ PDF Chat	Finite and Infinite Arithmetic Progressions Related to Beta-Expansion	2014	Bing Li Chao Ma
+ PDF Chat	Primes of the form 𝑝=1+𝑚²+𝑛² in short intervals	1998	Jie Wu
+	On digit frequencies in 𝛽-expansions	2016	Philip Boyland André de Carvalho Toby Hall
+	On sums and products of integers	1999	Yong-Gao Chen
+	Long Arithmetic Progressions in Sets with Small Sumset	2009	Itziar Bardají David J. Grynkiewicz
+	Long gaps between primes	2017	Kevin Ford Ben Green Sergeĭ Konyagin James Maynard Terence Tao
+ PDF Chat	A note on sum-free sets of integers	1980	Mên Ch’ang Hu
+ PDF Chat	Finding finite 𝐵₂-sequences with larger 𝑚-𝑎^{1/2}_{𝑚}	1994	Zhen Xiang Zhang
+ PDF Chat	Discrepancy in arithmetic progressions	1996	Jiřı́ Matoušek Joel Spencer

Works That Cite This (44)

Action	Title	Year	Authors
+ PDF Chat	Monochromatic Hilbert Cubes and Arithmetic Progressions	2019	József Balogh M. I. Lavrov George Shakan Adam Zsolt Wagner
+	A sharp inverse Littlewood-Offord theorem	2009	Terence Tao Van Vu
+	Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of $\mathbb{F_p}$	2021	Ali Alsetri Xuancheng Shao
+	On Hilbert cubes and primitive roots in finite fields	2021	Ali Alsetri Xuancheng Shao
+	None	2011	J.L. Rami ́rez Alfonsi ́n Sándor Z. Kiss Imre Z. Ruzsa Carlos Vinuesa
+	On Near-Linear-Time Algorithms for Dense Subset Sum	2020	Karl Bringmann Philip Wellnitz
+	Optimal inverse Littlewood–Offord theorems	2011	Hoi H. Nguyen Van Vu
+	A new approach to an old problem of Erdős and Moser	2012	Hoi H. Nguyen
+	A generalization of sumsets of set of integers	2014	Raj Kumar Mistri Ram Krishna Pandey
+ PDF Chat	Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition	2013	Khodakhast Bibak

Works Cited by This (28)

Action	Title	Year	Authors
+	Old and new problems and results in combinatorial number theory	1980	P. Erdős Ronald Graham
+	On addition of two distinct sets of integers	1995	Vsevolod F. Lev Pavel Smeliansky
+ PDF Chat	Unsolved Problems in Number Theory	1994	Richard K. Guy
+	Structure Theory of Set Addition	2018	Jean-Marc Deshouillérs Bernard Landreau A. A. Yudin
+	Combinatorial Number Theory	2009	Bruce Landman Melvyn B. Nathanson Jaroslav Nešetřil Richard J. Nowakowski Carl Pomerance Aaron Robertson
+	Combinatorial Number Theory	2013	Carl Pomerance Andràs Sárközy
+	Olson's theorem for cyclic groups	2005	Van Vu
+	On arithmetic progressions in sums of sets of integers	2012	Jean Bourgain
+	Arithmetic progressions in sumsets	2002	B. Green
+	Optimal Representations by Sumsets and Subset Sums	1997	Vsevolod F. Lev