Lessons in Enumerative Combinatorics

Lessons in Enumerative Combinatorics
Author :
Publisher : Springer Nature
Total Pages : 479
Release :
ISBN-10 : 9783030712501
ISBN-13 : 3030712508
Rating : 4/5 (508 Downloads)

Book Synopsis Lessons in Enumerative Combinatorics by : Ömer Eğecioğlu

Download or read book Lessons in Enumerative Combinatorics written by Ömer Eğecioğlu and published by Springer Nature. This book was released on 2021-05-13 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.

Lessons in Enumerative Combinatorics Related Books

Lessons in Enumerative Combinatorics
Language: en
Pages: 479
Authors: Ömer Eğecioğlu
Categories: Mathematics
Type: BOOK - Published: 2021-05-13 - Publisher: Springer Nature

GET EBOOK

This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and
A First Course in Enumerative Combinatorics
Language: en
Pages: 272
Authors: Carl G. Wagner
Categories: Education
Type: BOOK - Published: 2020-10-29 - Publisher: American Mathematical Soc.

GET EBOOK

A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate stude
Enumerative Combinatorics
Language: en
Pages: 632
Authors: Charalambos A. Charalambides
Categories: Business & Economics
Type: BOOK - Published: 2018-10-08 - Publisher: CRC Press

GET EBOOK

Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, in
Analytic Combinatorics
Language: en
Pages: 825
Authors: Philippe Flajolet
Categories: Mathematics
Type: BOOK - Published: 2009-01-15 - Publisher: Cambridge University Press

GET EBOOK

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent d
Introductory Combinatorics
Language: en
Pages: 648
Authors: Kenneth P. Bogart
Categories: Computers
Type: BOOK - Published: 1990 - Publisher: Harcourt Brace College Publishers

GET EBOOK

Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth B