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Everything about Arithmetic combinatorics
Mathematical subject
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Arithmetic combinatoricsA 5-minute orientation
- Skim a recent paper: Performance evaluation of solar hybrid combined cooling, heating and power systems: A multi-objective arithmetic optimization algorithmInfluential work since 2022
- Pick up a classic book: Computational Complexity of Counting and SamplingThe most-reprinted book on the subject
- Read the landmark paper: Evaluation of mental workload with a combined measure based on physiological indices during a dual task of tracking and mental arithmeticCited 347 times
- Go sideways: Szemerédi's theoremA closely related topic
- Go sideways: Ben Green (mathematician)A closely related topic
📖 Definitions
Noun A field of mathematics in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Evaluation of mental workload with a combined measure based on physiological indices during a dual task of tracking and mental arithmetic
Power monoids: A bridge between factorization theory and arithmetic combinatorics
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
Finite field models in arithmetic combinatorics – ten years on
Looking into Pascal's Triangle: Combinatorics, Arithmetic, and Geometry
From harmonic analysis to arithmetic combinatorics
Geometrical meaning of arithmetic series , and in terms of the elementary combinatorics
The arithmetic and combinatorics of buildings for 𝑆𝑝_{𝑛}
🆕 Influential since 2022
Performance evaluation of solar hybrid combined cooling, heating and power systems: A multi-objective arithmetic optimization algorithm
A novel study on forecasting the airfoil self-noise, using a hybrid model based on the combination of CatBoost and Arithmetic Optimization Algorithm
On some applications of GCD sums to arithmetic combinatorics
Arithmetic and Combinatorics of Recurrent Sequences
Arithmetic properties for sparse sequence of integers and its application in number theory, additive combinatorics and ergodic theory
📚 Books worth reading
Computational Complexity of Counting and SamplingIstvan Miklos · 2019
The Mathematics of Chip-FiringCaroline J. Klivans · 2018- 📕Integrability, Quantization, and GeometryI. M. Krichever · 2021
Axiomatic AnalysisRobert Katz · 1964
Davenport-Zannier Polynomials and Dessins D'EnfantsNikolai M. Adrianov, Fedor Pakovich · 2020- 📕Cluster algebra and Poisson geometryMichael Gekhtman · 2010
- 📕Mathematical Legacy of Richard P. StanleyPatricia Hersh, Thomas Lam · 2016
- 📕Discrete geometry and algebraic combinatoricsAlexander Barg, O. R. Musin · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Szemerédi's theorem In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured…
- Ben Green (mathematician) Ben Joseph Green FRS (born 27 February 1977) is a British mathematician specialising in combinatorics and number theory. He is the Waynflete Professor…
- Green–Tao theorem In number theory, the Green–Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long…
- Erdős–Szemerédi theorem In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set A of integers, at least one of the sets A+A and A⋅A (the sets…
- Vitaly Bergelson Vitaly Bergelson (born 1950 in Kiev) is a mathematical researcher and professor at Ohio State University in Columbus, Ohio. His research focuses on ergodic…
- Tamar Ziegler Tamar Debora Ziegler (Hebrew: תמר ציגלר; born 1971) is an Israeli mathematician specializing in Ergodic theory, Additive combinatorics and Number theory…
- 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…
- List of conjectures by Paul Erdős The prolific mathematician Paul Erdős and his various collaborators made many mathematical conjectures across subjects, and in many cases Erdős offered…