Introduction to Enumerative and Analytic Combinatorics

Bona Miklos
Innbundet / 2025 / Engelsk

Produktdetaljer

ISBN
9781032302706
Publisert
2025-03-11
Utgave
3. utgave
Utgiver
Vendor
Chapman & Hall/CRC
Vekt
1210 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
546

Forfatter
Bona Miklos

Biographical note

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.

Introduction to Enumerative and Analytic Combinatorics

Bona Miklos
Innbundet / 2025 / Engelsk
Bona Miklos
Innbundet / 2025 / Engelsk
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This 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.The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.Updates to the Third Edition include:Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter.A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book.An extended section on multivariate generating functions.Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation.The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association.
Les mer
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.
Les mer
Basic methodsWhen we add and when we subtractWhen we multiplyWhen we divideApplications of basic counting principlesThe pigeonhole principleNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesApplications of basic methodsMultisets and compositionsSet partitionsPartitions of integersThe inclusion-exclusion principleThe twelvefold wayNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesGenerating functionsPower seriesWarming up: Solving recurrence relationsProducts of generating functionsCompositions of generating functionsA different type of generating functionsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesTOPICSCounting permutationsEulerian numbersThe cycle structure of permutationsCycle structure and exponential generating functionsInversionsAdvanced applications of generating functions to permutation enumerationNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesCounting graphsTrees and forestsGraphs and functionsWhen the vertices are not freely labeledGraphs on colored verticesGraphs and generating functionsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesExtremal combinatoricsExtremal graph theoryHypergraphsSomething is more than nothing: Existence proofsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesAN ADVANCED METHODAnalytic combinatoricsExponential growth ratesPolynomial precisionMore precise asymptoticsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesSPECIAL TOPICSSymmetric structuresDesignsFinite projective planesError-correcting codesCounting symmetric structuresNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesSequences in combinatoricsUnimodalityLog-concavityThe real zeros propertyNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesCounting magic squares and magic cubesA distribution problemMagic squares of fixed sizeMagic squares of fixed line sumWhy magic cubes are differentNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesAppendix: The method of mathematical inductionWeak inductionStrong induction
Les mer

Relaterte produkter

This 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.The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.Updates to the Third Edition include:Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter.A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book.An extended section on multivariate generating functions.Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation.The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association.
Les mer
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.
Les mer
Basic methodsWhen we add and when we subtractWhen we multiplyWhen we divideApplications of basic counting principlesThe pigeonhole principleNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesApplications of basic methodsMultisets and compositionsSet partitionsPartitions of integersThe inclusion-exclusion principleThe twelvefold wayNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesGenerating functionsPower seriesWarming up: Solving recurrence relationsProducts of generating functionsCompositions of generating functionsA different type of generating functionsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesTOPICSCounting permutationsEulerian numbersThe cycle structure of permutationsCycle structure and exponential generating functionsInversionsAdvanced applications of generating functions to permutation enumerationNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesCounting graphsTrees and forestsGraphs and functionsWhen the vertices are not freely labeledGraphs on colored verticesGraphs and generating functionsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesExtremal combinatoricsExtremal graph theoryHypergraphsSomething is more than nothing: Existence proofsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesAN ADVANCED METHODAnalytic combinatoricsExponential growth ratesPolynomial precisionMore precise asymptoticsNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesSPECIAL TOPICSSymmetric structuresDesignsFinite projective planesError-correcting codesCounting symmetric structuresNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesSequences in combinatoricsUnimodalityLog-concavityThe real zeros propertyNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesCounting magic squares and magic cubesA distribution problemMagic squares of fixed sizeMagic squares of fixed line sumWhy magic cubes are differentNotesChapter reviewExercisesSolutions to exercisesSupplementary exercisesAppendix: The method of mathematical inductionWeak inductionStrong induction
Les mer

Produktdetaljer

ISBN
9781032302706
Publisert
2025-03-11
Utgave
3. utgave
Utgiver
Vendor
Chapman & Hall/CRC
Vekt
1210 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
546

Forfatter
Bona Miklos

Biographical note

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.

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