Jukna Stasys Extremal Combinatorics / With Applications in Computer Science 9783540663133

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Автор: Jukna Stasys
Название: Extremal Combinatorics / With Applications in Computer Science
ISBN: 9783540663133
Издательство: Springer
Классификация:

Математические основы

Комбинаторика и теория графов

ISBN-10: 3540663134
Обложка/Формат: Hardback
Страницы: 392
Вес: 0.75 кг.
Дата издания: 01.02.2000
Серия: Texts in Theoretical Computer Science. An EATCS Series
Язык: English
Иллюстрации: With 36 figs. and 315 exercises.
Размер: 24.08 x 16.41 x 2.72 cm
Читательская аудитория: Professional & vocational
Подзаголовок: With applications in computer science
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The book is a concise, self-contained and up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called gems of the theory. A wide spectrum of most powerful combinatorial tools is presented: methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A throughout discussion of some recent applications to computer science motivates the liveliness and inherent usefulness of these methods to approach problems outside combinatorics. No special combinatorial or algebraic background is assumed. All necessary elements of linear algebra and discrete probability are introduced before their combinatorial applications. Aimed primarily as an introductory text for graduates, it provides also a compact source of modern extremal combinatorics for researchers in computer science and other fields of discrete mathematics.
Дополнительное описание: Формат: 235x155
Илюстрации: 36
Круг читателей: Graduate and undergraduate students, scientists,researchers, lecturers and tutors in mathematics, computerscience and engineering
Ключевые слова: Diskrete Mathematik
Kombinatorik
combinatorics
computational complexity
discrete mathematics
extremal combinatorics
extremal set theory
Язык: eng
Оглавление: Introduction.- I. The Classis: Counting.- The Pigeon-Hole Principle.- Principle of Inclusion and Exclusion.- Systems of Distinct Representatives.- Colorings.- Chains and Antichains.- Intersecting Families.- Covers and Transversals.- Sunflowers.- Density and Universality.- Designs.- Witness Sets.- Isolation Lemmas.- II. The Linear Algebra Method: Basic Method.- The Polynomial Technique.- Monotone Span Programs.- III. The Probabilistic Method: Basic Tools.- Counting Sieve.- LovГЎsz Sieve.- Linearity of Expectation.- The Deletion Method.- Second Moment Method.- Bounding of Large Deviations.- Randomized Algorithms.- Derandomization.- The Entropy Function.- Random Walks and Search Problems.- IV. Fragments of Ramsey Theory: Ramsey's Theorem.- The Hales-Jewett Theorem.- Epilogue: What Next?- Bibliography.- Index.

Extremal Combinatorics / With Applications in Computer Science, Jukna Stasys