{"product_id":"lessons-in-enumerative-combinatorics-paperback","title":"Lessons in Enumerative Combinatorics - Paperback","description":"\u003cp\u003eby \u003cb\u003eÖmer Eğecioğlu\u003c\/b\u003e (Author), \u003cb\u003eAdriano M. Garsia\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e1. 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.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eBeginning 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLessons in Enumerative Combinatorics\u003c\/i\u003e 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.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eÖmer Eğecioğlu\u003c\/b\u003e is Professor of Computer Science at the University of California, Santa Barbara. His research interests include bijective and enumerative combinatorics, algorithms, and computational geometry.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAdriano Garsia\u003c\/b\u003e 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.\u003c\/p\u003e \u003cp\u003eTogether, the authors have previously published \u003ci\u003eLectures in Algebraic Combinatorics\u003c\/i\u003e (2020) in the series \u003cb\u003eLecture Notes in Mathematics\u003c\/b\u003e.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 479\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 14, 2022\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42718495375423,"sku":"9783030712525","price":106.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/7bb1894a504387f7611a4e23e0187954.webp?v=1765082160","url":"https:\/\/dhlswag.com\/products\/lessons-in-enumerative-combinatorics-paperback","provider":"BBB","version":"1.0","type":"link"}