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.
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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Miklós Bónareceived 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
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
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