000			03105nam a22003377a 4500
003			OSt
005			20241017111405.0
008			241016b |||||||| |||| 00| 0 hin d
020			_a9783030712525
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a519.11 _bEGE-L
100			_aEğecioğlu, Ömer
245			_aLessons in enumerative combinatorics
260			_aSwitzerland : _bSpringer, _c2021.
300			_axvi, 479p. : _b329 illus., 3 illus. in color.
490			_aGraduate texts in mathematics, _v290 _x0072-5285
504			_aIncludes bibliographical references and index.
520			_aThis 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.
650			_aDiscrete Mathematics
650			_aLogic, Symbolic and mathematical
650			_aCombinatorics
650			_aBijective proofs
650			_aLagrange Inversion
650			_aGraph coloring
650			_aCombinatorics computer science
700			_aGarsia, Adriano M.
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-71250-1/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/71331738-lessons-in-enumerative-combinatorics?from_search=true&from_srp=true&qid=7NLmRQYFgq&rank=1#CommunityReviews
942			_cBK _2udc
999			_c35299 _d35299