Extremal problems for finite sets

著者

• Frankl, Peter
• 徳重, 典英 トクシゲ, ノリヒデ

書誌事項

Extremal problems for finite sets

Peter Frankl, Norihide Tokushige

（Student mathematical library, v. 86）

American Mathematical Society, c2018

注記

Includes bibliographical references (p. 217-222) and index

内容説明・目次

内容説明

One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study. The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede-Khachatrian theorem as well as some recent progress on the Erdos matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza-Erdos-Frankl theorem, application of Rodl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdos-Szemeredi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.

目次

Introduction Operations on sets and set systems Theorems on traces The Erdos-Ko-Rado theorem via shifting Katona's circle The Kurskal-Katona theorem Kleitman theorem for no $s$ pairwise disjoint sets The Hilton-Milner theorem The Erdos matching conjecture The Ahswede-Khachatrian theorem Pushing-pulling method Uniform measure versus product measure Kleitman's correlation inequality $r$-cross union families Random walk method $L$-systems Exponent of $(10,\{0,1,3,6\})$-system The Deza-Erdos-Frankl theorem Furedi's structure theorem Rodl's packing theorem Upper bounds using multilinear polynomials Application to discrete geometry Upper bounds using inclusion matrices Some algebraic constructions for $L$-systems Oddtown and eventown problems Tensor product method The ratio bound Measures of cross independent sets Application of semidefinite programming A cross intersection problem with measures Capsets and sunflowers Challenging open problems Bibliography Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB26670032
• ISBN:
  • 9781470440398
• LCCN: 2017061643
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: viii, 224 p.
• 大きさ: 22 cm
• 分類:
  • LCC : QA295
  • DC23 : 511/.6
• 件名:
  • LCSH : Extremal problems (Mathematics)
  • LCSH : Set theory
• 親書誌ID:
  • BA42504671