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Lessons in enumerative combinatorics

Egecioglu, Omer.

Lessons in enumerative combinatorics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lessons in enumerative combinatoricsby Omer Egecioglu, Adriano M. Garsia.
作者:	Egecioglu, Omer.
其他作者:	Garsia, Adriano M.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xvi, 479 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Combinatorial analysis.
電子資源:	https://doi.org/10.1007/978-3-030-71250-1
ISBN:	9783030712501$q(electronic bk.)

Lessons in enumerative combinatorics
Egecioglu, Omer.

Lessons in enumerative combinatorics[electronic resource] /by Omer Egecioglu, Adriano M. Garsia. - Cham :Springer International Publishing :2021. - xvi, 479 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2900072-5285 ;. - Graduate texts in mathematics ;129..

1. Basic Combinatorial Structures -- 2. Partitions and Generating Functions -- 3. Planar Trees and the Lagrange Inversion Formula -- 4. Cayley Trees -- 5. The Cayley-Hamilton Theorem -- 6. Exponential Structures and Polynomial Operators -- 7. The Inclusion-Exclusion Principle -- 8. Graphs, Chromatic Polynomials and Acyclic Orientations -- 9. Matching and Distinct Representatives.

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.

ISBN: 9783030712501$q(electronic bk.)

Standard No.: 10.1007/978-3-030-71250-1doiSubjects--Topical Terms:

182280
Combinatorial analysis.

LC Class. No.: QA164 / .E3174 2021

Dewey Class. No.: 511.6

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520 $a 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.
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