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On the approximate structure of sets whose sumset is small
In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose
Freiman's_theorem
Russian and Israeli mathematician (1926–2024)
theory, in particular, for proving Freiman's theorem. He was a professor emeritus in Tel Aviv University. Freiman was born in Kazan on 3 July 1926. He
Gregory_Freiman
theorem (number theory) Fermat polygonal number theorem (number theory) Five color theorem (graph theory) Four color theorem (graph theory) Freiman's
List_of_theorems
Set of pairwise sums of elements of two sets
small (compared to the size of A {\displaystyle A} ); see for example Freiman's theorem. Restricted sumset Sidon set Sum-free set Schnirelmann density Shapley–Folkman
Sumset
Mathematical subject
result can be seen as a nonabelian version of Freiman's theorem, and a generalization of Gromov's theorem on groups of polynomial growth. If A is a set
Arithmetic_combinatorics
Area of combinatorics in mathematics
structures of A and B? In the case of the integers, the classical Freiman's theorem provides a partial answer to this question in terms of multi-dimensional
Additive_combinatorics
Topics referred to by the same term
Schwabing, Munich, Germany Freiman Mall, Ottawa, Canada Freimans, a defunct department store in Ottawa, Canada Alexander Freiman (1879–1968), Polish/Soviet
Freimann
Proof assistant and programming language
Inductive Constructions), the foundational type theory developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source
Lean_(proof_assistant)
American mathematician
work, A polynomial bound in Freiman's theorem, Professor Chang established new quantitative bounds for Freiman's inverse theorem. Mei-Chu Chang was elected
Mei-Chu_Chang
Mathematical problem
Erdős–Ginzburg–Ziv theorem after its discoverers. It may also be deduced from the Cauchy–Davenport theorem. More general results than this theorem exist, such
Zero-sum_problem
British mathematician
progressions, for his work dramatically improving bounds connected with Freiman's theorem on sets with small doubling, and for other results in additive combinatorics
Tom_Sanders_(mathematician)
Type of numeric sequence
semilinear sets are exactly the sets definable in Presburger arithmetic. Freiman's theorem Tao & Vu 2006, p. xvii, Definition 0.2 (Progressions). Tao and Vu
Generalized arithmetic progression
Generalized_arithmetic_progression
Interactive theorem prover software
computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs
Proof_assistant
Hungarian mathematician
(log x)1+ε elements up to x, for every x. He gave a new proof to Freiman's theorem. Ruzsa also showed the existence of a Sidon sequence which has at
Imre_Z._Ruzsa
the inequality. The inequality forms a crucial step in the proof of Freiman's theorem. The following sumset notation is standard in additive combinatorics
Plünnecke–Ruzsa_inequality
Hungarian mathematician (1941–2019)
com/2007/03/11/ben-green-the-polynomial-freiman-ruzsa-conjecture/ Ruzsa, I. (1999). "An analog of Freiman's theorem in groups" (PDF). Astérisque. 258: 323–326
Katalin_Marton
In additive number theory, a way to measure how dense a sequence of numbers is
this theorem for lower asymptotic density was obtained by Kneser. At a later date, E. Artin and P. Scherk simplified the proof of Mann's theorem. Let
Schnirelmann_density
One of several related theorems regarding the sizes of certain sumsets in abelian groups
mathematics known as additive combinatorics, Kneser's theorem can refer to one of several related theorems regarding the sizes of certain sumsets in abelian
Kneser's theorem (combinatorics)
Kneser's_theorem_(combinatorics)
Sumset of a field subject to a specific polynomial restriction
Cauchy-Davenport Theorem for Finite Groups". arXiv:1202.1816 [math.CO]. DeVos, Matt (2016). "On a Generalization of the Cauchy-Davenport Theorem". Integers
Restricted_sumset
Complicated set of real numbers
y)|\right)^{-1}:f(x,y)=ax^{2}+bxy+cy^{2},\ b^{2}-4ac=1\right\}} Starting from Hurwitz's theorem on Diophantine approximation, that any real number ξ {\displaystyle \xi
Markov_spectrum
Month of 1926
during a drizzling rain. Born: Gregory Freiman, Russian-born Israeli mathematician known for Freiman's theorem; in Kazan, Tatar ASSR, Russian SFSR, Soviet
July_1926
British mathematician (born 1977)
with Terence Tao, they proved a structure theorem for approximate groups, generalising the Freiman-Ruzsa theorem on sets of integers with small doubling
Ben_Green_(mathematician)
Soviet mathematician
7 November 1968) was a Soviet mathematician. Gelfond's theorem, also known as the Gelfond–Schneider theorem, is named after him. Alexander Gelfond was born in
Alexander_Gelfond
Mathematical concept
Green 2012, Theorem 2.1. Breuillard, Tao & Green 2012, Theorem 1.6. Breuillard 2012, Theorem 4.8. Breuillard, Tao & Green 2012, Theorem 1.11. Breuillard
Approximate_group
Mathematics used in ancient Mesopotamia
fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian tablet YBC 7289 gives an approximation of 2 {\displaystyle
Babylonian_mathematics
Israeli academic
with Paul Erdős and Abraham Ziv, proved the Erdős-Ginzburg-Ziv Theorem. This Theorem is an important result in Abelian group theory, and is cited to
Abraham_Ginzburg
Property of an irrational number
{\displaystyle \alpha } is the factor for which Dirichlet's approximation theorem can be improved for α {\displaystyle \alpha } . Certain numbers can be
Markov_constant
Cube that fits through hole in smaller cube
rectangle equal ( 3 2 ) / 4 {\textstyle (3{\sqrt {2}})/4} , by the Pythagorean theorem or (equivalently) the formula for Euclidean distance in three dimensions
Prince_Rupert's_cube
Form of scientific experiment
Epidemiologic Reviews. 24 (1): 39–53. doi:10.1093/epirev/24.1.39. PMID 12119854. Freiman JA, Chalmers TC, Smith H, et al. (September 1978). "The importance of beta
Randomized_controlled_trial
Borough in New Jersey, United States
Princeton Andrew Wiles (born 1953), mathematician who proved Fermat's Last Theorem, Princeton University professor Woodrow Wilson (1856–1924), 28th President
Princeton,_New_Jersey
scientist and translator Kenneth Appel (1932–2013), proved four-color theorem Zvi Arad (1942–2018), mathematician Vladimir Arnold (1937–2010), mathematician;
List_of_Jewish_mathematicians
FREIMANS THEOREM
FREIMANS THEOREM
Girl/Female
American, British, English
Freeman; Feminine Variant of Charles; Manly
Male
English
 English name originally derived from the name of a Germanic tribe called the Franks, FRANK means "French." It is also used as a short form of Franklin "freeman" and Francis "French."Â
Male
English
Variant spelling of English Franklin, FRANKLYN means "freeman."
Boy/Male
American, Anglo, Australian, British, Christian, English
Free Man
Boy/Male
Christian & English(British/American/Australian)
A Freeman
Male
English
 Anglicized form of Irish Gaelic Conn, having several possible CORNELIUS meanss including "chief, freeman, head, hound, intelligence, strength." Compare with another form of Cornelius.
Surname or Lastname
English
English : variant of Free.Irish : Anglicized (‘translated’) form of Gaelic Ó Saoraidhe (see Seery).In New England, an English equivalent of French Foissy (see Foisy).Translation of German Freimann (see Freiman).
Surname or Lastname
English
English : unexplained; possibly a variant of Burdett.Robert Burdick was a freeman of Newport, RI, in 1655.
Boy/Male
American, Australian, British, Celtic, English, Irish, Norse
Freeman; Park with Deer
Boy/Male
American, Australian, British, Christian, English, German, Jamaican
Chipping Sparrow; Man; Strong Man; A Freeman
Male
English
English surname transferred to forename use, FREEMAN means "freeman."
Boy/Male
American, Australian, British, Celtic, Chinese, Christian, English, Gaelic, German, Greek, Irish, Latin, Scottish
Wisdom; Chief; Wise; Counsel; Reason; Intelligence; Surname; Freeman; Head; Hound; Strength; Fifth
Boy/Male
African, American, Anglo, Australian, British, Chinese, Christian, English, French, German, Hebrew, Indian, Jamaican, Teutonic
Nobleman; The Title of Nobility Used as a First Name; Freeman; Young Warrior
Surname or Lastname
English, German, Danish, and Jewish (Ashkenazic)
English, German, Danish, and Jewish (Ashkenazic) : variant of Wild.Thomas Wilder is recorded as a freeman of Charlestown, MA, in 1640. He had numerous prominent descendents.
Male
English
English surname transferred to forename use, from the Middle English word frankeleyn, FRANKLIN means "freeman."Â
Girl/Female
American, Australian, Chinese
Derivative of Imani; Faith; Freeman; Associated to Goddess Durga
Male
Irish
Old Irish name derived from Gaelic conn, having several possible CONN meanss including "chief, freeman, head, hound, intelligence, strength."
Surname or Lastname
English
English : patronymic from Stern 2.In 1646 Charles Stearns was admitted as a freeman of Watertown, MA.
Boy/Male
French
Free man; a man freed from bound servitude to an overlord. Surname.
Girl/Female
American, Anglo, Australian, British, English, German, Jamaican
Combination of Cara and Lynn; Manly; Feminine Diminutive Form of Charles; Carl; Freeman; Beloved
FREIMANS THEOREM
FREIMANS THEOREM
FREIMANS THEOREM
FREIMANS THEOREM
FREIMANS THEOREM
FREIMANS THEOREM
FREIMANS THEOREM