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Extremal Problems for Finite Sets

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name:Extremal Problems for Finite Sets
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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 Erd s matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza Erd s Frankl theorem, application of Rödl’s packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erd s Szemerédi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
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类别:Books
语言:English  English
总大小:1.47 MB
哈希信息:998137C9797E52DE1C5AD88C6771F0761CE2AB67
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加入的日期:2018-11-10 18:31:16
洪流地位:Torrent Verified


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