Miklos Bona

Introduction to Enumerative and Analytic Combinatorics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

These award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author's goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Erscheinungstermin: 11. März 2025
• Englisch
• ISBN-13: 9781040312179
• Artikelnr.: 72811838

Autorenporträt

Miklós Bóna received his Ph.D in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bóna has mentored numerous graduate and undergraduate students. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an Editor-in-Chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.

Inhaltsangabe

Basic methodsWhen we add and when we subtractWhen we multiplyWhen we divide
Applications of basic counting principlesThe pigeonhole principleNotes
Chapter reviewExercisesSolutions to exercisesSupplementary exercises
Applications of basic methodsMultisets and compositionsSet partitions
Partitions of integersThe inclusion-exclusion principleThe twelvefold way
NotesChapter reviewExercisesSolutions to exercisesSupplementary exercises
Generating functionsPower seriesWarming up: Solving recurrence relations
Products of generating functionsCompositions of generating functionsA
different type of generating functionsNotesChapter reviewExercises
Solutions to exercisesSupplementary exercises
TOPICS
Counting permutationsEulerian numbersThe cycle structure of permutations
Cycle structure and exponential generating functionsInversionsAdvanced
applications of generating functions to permutation enumerationNotes
Chapter reviewExercisesSolutions to exercisesSupplementary exercises
Counting graphsTrees and forestsGraphs and functionsWhen the vertices are
not freely labeledGraphs on colored verticesGraphs and generating functions
NotesChapter reviewExercisesSolutions to exercisesSupplementary exercises
Extremal combinatoricsExtremal graph theoryHypergraphsSomething is more
than nothing: Existence proofsNotesChapter reviewExercisesSolutions to
exercisesSupplementary exercises
AN ADVANCED METHOD
Analytic combinatoricsExponential growth ratesPolynomial precision
More precise asymptoticsNotesChapter reviewExercisesSolutions to exercises
Supplementary exercises
SPECIAL TOPICS
Symmetric structuresDesignsFinite projective planesError-correcting codes
Counting symmetric structuresNotesChapter reviewExercisesSolutions to
exercisesSupplementary exercises
Sequences in combinatoricsUnimodality
Log-concavity
The real zeros property
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Counting magic squares and magic cubesA distribution problem
Magic squares of fixed size
Magic squares of fixed line sum
Why magic cubes are different
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Appendix: The method of mathematical induction
Weak induction
Strong induction