| Softcover ISBN: | 978-1-4704-4039-8 |
| Product Code: | STML/86 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-4847-9 |
| Product Code: | STML/86.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-1-4704-4039-8 |
| eBook: ISBN: | 978-1-4704-4847-9 |
| Product Code: | STML/86.B |
| List Price: | $108.00 $83.50 |
| Softcover ISBN: | 978-1-4704-4039-8 |
| Product Code: | STML/86 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-4847-9 |
| Product Code: | STML/86.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-1-4704-4039-8 |
| eBook ISBN: | 978-1-4704-4847-9 |
| Product Code: | STML/86.B |
| List Price: | $108.00 $83.50 |
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Book DetailsStudent Mathematical LibraryVolume: 86; 2018; 232 ppMSC: Primary 05
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 Erdős matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza–Erdős–Frankl theorem, application of Rödl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdős–Szemerédi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
ReadershipUndergraduate students interested in discrete mathematics and combinatorics.
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Table of Contents
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Chapters
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Introduction
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Operations on sets and set systems
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Theorems on traces
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The Erdős-Ko-Rado theorem via shifting
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Katona’s circle
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The Kurskal-Katona theorem
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Kleitman theorem for no $s$ pairwise disjoint sets
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The Hilton-Milner theorem
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The Erdős matching conjecture
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The Ahswede-Khachatrian theorem
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Pushing-pulling method
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Uniform measure versus product measure
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Kleitman’s correlation inequality
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$r$-cross union families
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Random walk method
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$L$-systems
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Exponent of $(10,\{0,1,3,6\})$-system
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The Deza-Erdős-Frankl theorem
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Füredi’s structure theorem
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Rödl’s packing theorem
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Upper bounds using multilinear polynomials
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Application to discrete geometry
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Upper bounds using inclusion matrices
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Some algebraic constructions for $L$-systems
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Oddtown and eventown problems
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Tensor product method
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The ratio bound
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Measures of cross independent sets
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Application of semidefinite programming
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A cross intersection problem with measures
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Capsets and sunflowers
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Challenging open problems
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Additional Material
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Reviews
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No existing book has similar coverage.
D. V. Feldman, CHOICE -
[This book] makes cutting-edge results reasonably accessible to undergraduates...I am not aware of any other source for this material that allows well-prepared undergraduates to get up to speed in this area of mathematics.
Mark Hunacek, MAA Reviews
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 Erdős matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza–Erdős–Frankl theorem, application of Rödl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdős–Szemerédi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
Undergraduate students interested in discrete mathematics and combinatorics.
-
Chapters
-
Introduction
-
Operations on sets and set systems
-
Theorems on traces
-
The Erdős-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 Erdős 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-Erdős-Frankl theorem
-
Füredi’s structure theorem
-
Rödl’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
-
No existing book has similar coverage.
D. V. Feldman, CHOICE -
[This book] makes cutting-edge results reasonably accessible to undergraduates...I am not aware of any other source for this material that allows well-prepared undergraduates to get up to speed in this area of mathematics.
Mark Hunacek, MAA Reviews
