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Statements

Subject Item
dbr:Ben_Green_(mathematician)
dbo:wikiPageWikiLink
dbr:Polynomial_method_in_combinatorics
Subject Item
dbr:Restricted_sumset
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dbr:Polynomial_method_in_combinatorics
Subject Item
dbr:Combinatorics
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dbr:Polynomial_method_in_combinatorics
Subject Item
dbr:Szemerédi–Trotter_theorem
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dbr:Polynomial_method_in_combinatorics
Subject Item
dbr:Polynomial_method_in_combinatorics
rdfs:label
Polynomial method in combinatorics
rdfs:comment
In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently, the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems. The polynomial method encompasses a wide range of specific techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such as Alon's Combinatorial Nullstellensatz, have been known since the 1990s, it was not until around 2010 that a broader framework for the polynomial method has been developed.
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dbc:Combinatorics
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dbr:Schwartz–Zippel_lemma dbr:Restricted_sumset dbr:Combinatorics dbr:Szemerédi–Trotter_theorem dbc:Combinatorics dbr:Homogeneous_polynomial dbr:Ham_sandwich_theorem dbr:Cap_set dbr:Erdős_distinct_distances_problem dbr:Kakeya_set
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n13:1310.6482 n14:erdossurvey.pdf
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dbo:abstract
In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently, the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems. The polynomial method encompasses a wide range of specific techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such as Alon's Combinatorial Nullstellensatz, have been known since the 1990s, it was not until around 2010 that a broader framework for the polynomial method has been developed.
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wikipedia-en:Polynomial_method_in_combinatorics?oldid=1118038735&ns=0
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wikipedia-en:Polynomial_method_in_combinatorics
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