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Everything about Zero-sum problem
Mathematical 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 abelian group G and a positive integer n, one asks for the smallest value of k such that every sequence of elements of G of size k contains n terms that sum to 0. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Zero-sum problemA 5-minute orientation
- Skim a recent paper: Solving the Zero-Sum Control Problem for Tidal Turbine System: An Online Reinforcement Learning ApproachInfluential work since 2022
- Pick up a classic book: The Answer to EverythingThe most-reprinted book on the subject
- Read the landmark paper: Designing Zero-Gradient-Sum Protocols for Finite-Time Distributed Optimization ProblemCited 62 times
- Go sideways: Barycentric-sum problemA closely related topic
- Go sideways: Restricted sumsetA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
No outline available.
🏆 Landmark papers (most cited)
Designing Zero-Gradient-Sum Protocols for Finite-Time Distributed Optimization Problem
Zero-sum state constrained differential games: existence of value for Bolza problem
Inverse zero-sum problems
A generalization of a classical zero-sum problem
On a discrete-time non-zero-sum Dynkin problem with monotonicity
Note on a Zero-Sum Problem
NON-ZERO-SUM GAMES RELATED TO THE SECRETARY PROBLEM
On a discrete-time non-zero-sum Dynkin problem with monotonicity
🆕 Influential since 2022
Solving the Zero-Sum Control Problem for Tidal Turbine System: An Online Reinforcement Learning Approach
A Partially Observable Stochastic Zero-sum Game for a Network Epidemic Control Problem
An addendum to the problem of zero-sum LQ stochastic mean-field dynamic games
ON MONOIDS OF PLUS-MINUS WEIGHTED ZERO-SUM SEQUENCES: THE ISOMORPHISM PROBLEM AND THE CHARACTERIZATION PROBLEM
Output Feedback Q-Learning for a Non-Zero-Sum Game Problem in Building HVAC Control
📚 Books worth reading
- 📕The Answer to EverythingCanon · 2026
- 📕Horizons of Fractal Geometry and Complex DimensionsRobert G. Niemeyer · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Barycentric-sum problem Combinatorial number theory deals with number theoretic problems which involve combinatorial ideas in their formulations or solutions. Paul Erdős is the…
- 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 , ……
- Zero-sum Ramsey theory In mathematics, zero-sum Ramsey theory or zero-sum theory is a branch of combinatorics. It deals with problems of the following kind: given a combinatorial…
- Kemnitz's conjecture In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also…
- Additive number theory Additive number theory is the subfield of number theory concerning the study of subsets of integers and their behavior under addition. More abstractly…
- 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…
- Abraham Ginzburg Abraham Ginzburg (Hebrew: אברהם גינזבורג) (1926–2020) was a Professor Emeritus of Computer Science. He served as Vice President of the Technion Institute…
- Additive combinatorics Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are inverse problems: given the size…