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Lessons in Enumerative Combinatorics (Paperback, 1st ed. 2021)
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Lessons in Enumerative Combinatorics (Paperback, 1st ed. 2021)
Series: Graduate Texts in Mathematics, 290
Expected to ship within 18 - 22 working days
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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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