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Everything about Additive combinatorics
Area of combinatorics in mathematics
Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are inverse problems: given the size of the sumset A + B is small, what can we say about the 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 arithmetic progressions. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Additive combinatoricsA 5-minute orientation
- Skim a recent paper: A Faster Exponential Time Algorithm for Bin Packing With a Constant Number of Bins via Additive CombinatoricsInfluential work since 2022
- Pick up a classic book: Additive combinatoricsThe most-reprinted book on the subject
- Read the landmark paper: Health benefits of fruit and vegetables are from additive and synergistic combinations of phytochemicalsCited 1,549 times
- Go sideways: Freiman's theoremA closely related topic
- Go sideways: Arithmetic combinatoricsA closely related topic
📖 Definitions
Noun A subbranch of combinatorics that concerns additive problems expressed using sumsets.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Health benefits of fruit and vegetables are from additive and synergistic combinations of phytochemicals
Non-Malleable Codes from Additive Combinatorics
On Linear Combinatorics II. Structure Theorems via Additive Number Theory
Some additive combinatorics problems in matrix rings
Equivalence of polynomial conjectures in additive combinatorics
Non-commutative methods in additive combinatorics and number theory
An Additive Combinatorics Approach Relating Rank to Communication Complexity
Three convolution inequalities on the real line with connections to additive combinatorics
🆕 Influential since 2022
A Faster Exponential Time Algorithm for Bin Packing With a Constant Number of Bins via Additive Combinatorics
Exponential mixing via additive combinatorics
Hilbert’s tenth problem via additive combinatorics
Information Inequalities via Ideas From Additive Combinatorics
An effective local-global principle and additive combinatorics in finite fields
📚 Books worth reading
- 📕Additive combinatoricsTerence Tao · 2010
Additive combinatoricsTerence Tao · 2010- 📕Additive combinatoricsTerence Tao · 2010
Combinatorial number theory and additive group theoryAlfred Geroldinger · 2009
Additive combinatoricsAndrew Granville, Melvyn B. Nathanson · 2007
ADDITIVE COMBINATORICSTerence Tao · 2006- 📕Structural additive theoryDavid J. Grynkiewicz · 2013
- 📕Galois theories of linear difference equationsCharlotte Hardouin · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Freiman's theorem In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose…
- Arithmetic combinatorics In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Arithmetic…
- Plünnecke–Ruzsa inequality In additive combinatorics, the Plünnecke–Ruzsa inequality is an inequality that bounds the size of various sumsets of a set B, given that there is another…
- Zero-sum problem In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite…
- Ruzsa triangle inequality In additive combinatorics, the Ruzsa triangle inequality, also known as the Ruzsa difference triangle inequality to differentiate it from some of its variants…
- Restricted sumset In additive number theory and combinatorics, a restricted sumset has the form S = { a 1 + ⋯ + a n : a 1 ∈ A 1 , … , a n ∈ A n a n d P ( a 1 , ……
- Kneser's theorem (combinatorics) In the branch of mathematics known as additive combinatorics, Kneser's theorem can refer to one of several related theorems regarding the sizes of certain…
- Generalized arithmetic progression In mathematics, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an arithmetic progression equipped with…