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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.
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.
Ömer E¿eciölu is Professor of Computer Science at the University of California, Santa Barbara. His research interests include bijective and enumerative combinatorics, algorithms, and computational geometry.
Adriano Garsia is Professor Emeritus of Mathematics at the University of California, San Diego. He is renowned for his contributions to algebraic combinatorics, representation theory, and analysis. His wide-ranging research achievements are complemented by a lifelong enthusiasm for teaching and mentoring.
Together, the authors have previously published Lectures in Algebraic Combinatorics (2020) in the series Lecture Notes in Mathematics.
Offers a unified and friendly approach to enumerative combinatorics through formal languages
Showcases the authors' unique perspective and insightful examples
Illuminates the important connection between discrete mathematics and computer science
Engages readers through numerous exercises, examples, and applications
| Erscheinungsjahr: | 2021 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 496 |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xvi
479 S. 326 s/w Illustr. 3 farbige Illustr. 479 p. 329 illus. 3 illus. in color. |
| ISBN-13: | 9783030712495 |
| ISBN-10: | 3030712494 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Garsia, Adriano M.
E¿ecio¿lu, Ömer |
| Auflage: | 1st ed. 2021 |
| Hersteller: |
Springer International Publishing
Graduate Texts in Mathematics |
| Maße: | 241 x 160 x 31 mm |
| Von/Mit: | Adriano M. Garsia (u. a.) |
| Erscheinungsdatum: | 13.05.2021 |
| Gewicht: | 0,994 kg |
Ömer E¿eciölu is Professor of Computer Science at the University of California, Santa Barbara. His research interests include bijective and enumerative combinatorics, algorithms, and computational geometry.
Adriano Garsia is Professor Emeritus of Mathematics at the University of California, San Diego. He is renowned for his contributions to algebraic combinatorics, representation theory, and analysis. His wide-ranging research achievements are complemented by a lifelong enthusiasm for teaching and mentoring.
Together, the authors have previously published Lectures in Algebraic Combinatorics (2020) in the series Lecture Notes in Mathematics.
Offers a unified and friendly approach to enumerative combinatorics through formal languages
Showcases the authors' unique perspective and insightful examples
Illuminates the important connection between discrete mathematics and computer science
Engages readers through numerous exercises, examples, and applications
| Erscheinungsjahr: | 2021 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 496 |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xvi
479 S. 326 s/w Illustr. 3 farbige Illustr. 479 p. 329 illus. 3 illus. in color. |
| ISBN-13: | 9783030712495 |
| ISBN-10: | 3030712494 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Garsia, Adriano M.
E¿ecio¿lu, Ömer |
| Auflage: | 1st ed. 2021 |
| Hersteller: |
Springer International Publishing
Graduate Texts in Mathematics |
| Maße: | 241 x 160 x 31 mm |
| Von/Mit: | Adriano M. Garsia (u. a.) |
| Erscheinungsdatum: | 13.05.2021 |
| Gewicht: | 0,994 kg |
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