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Graph theory and additive combinatorics = exploring structure and randomness /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Graph theory and additive combinatorics/ Yufei Zhao.
其他題名:	exploring structure and randomness /
作者:	Zhao, Yufei,
出版者:	Cambridge ; New York, NY :Cambridge University Press, : 2023.,
面頁冊數:	xvii, 316 p. :ill., digital ; : 26 cm.;
附註:	Title from publisher's bibliographic system (viewed on 10 Aug 2023).
標題:	Additive combinatorics. -
電子資源:	https://doi.org/10.1017/9781009310956
ISBN:	9781009310956

Graph theory and additive combinatorics = exploring structure and randomness /
Zhao, Yufei,1988-

Graph theory and additive combinatoricsexploring structure and randomness /[electronic resource] :Yufei Zhao. - Cambridge ; New York, NY :Cambridge University Press,2023. - xvii, 316 p. :ill., digital ;26 cm.

Title from publisher's bibliographic system (viewed on 10 Aug 2023).

Appetizer : triangles and equations -- Forbidding a subgraph -- Graph regularity method -- Pseudorandom graphs -- Graph limits -- Graph homomorphism inequalities -- Forbidding 3-term arithmetic progressions -- Structure of set addition -- Sum-product problem -- Progressions in sparse pseudorandom sets.

Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

ISBN: 9781009310956Subjects--Topical Terms:

1076684
Additive combinatorics.

LC Class. No.: QA166 / .Z54 2023

Dewey Class. No.: 511.5

Graph theory and additive combinatorics = exploring structure and randomness /
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300 $a xvii, 316 p. : $b ill., digital ; $c 26 cm.
500 $a Title from publisher's bibliographic system (viewed on 10 Aug 2023).
505 0 $a Appetizer : triangles and equations -- Forbidding a subgraph -- Graph regularity method -- Pseudorandom graphs -- Graph limits -- Graph homomorphism inequalities -- Forbidding 3-term arithmetic progressions -- Structure of set addition -- Sum-product problem -- Progressions in sparse pseudorandom sets.
520 $a Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.
650 0 $a Additive combinatorics. $3 1076684
650 0 $a Graph theory. $3 527884
856 4 0 $u https://doi.org/10.1017/9781009310956