Handbook of enumerative combinatorics. (2015)

• Record Type: Book
• Other Titles: Enumerative combinatorics
• Further Information: Note: Edited by Miklos Bona.
• Editors: Bóna, Miklós
• Contents: METHODS; ; Algebraic and Geometric Methods in Enumerative Combinatorics; Introduction; What is a Good Answer?; Generating Functions; Linear Algebra Methods; Posets; Polytopes; Hyperplane Arrangements; Matroids; Acknowledgments; ; Analytic Methods ; Helmut Prodinger ; Introduction; Combinatorial Constructions and Associated Ordinary Generating Functions; Combinatorial Constructions and Associated Exponential Generating Functions; Partitions and Q-Series; Some Applications of the Adding a Slice Technique; Lagrange Inversion Formula; Lattice Path Enumeration: The Continued Fraction Theorem; Lattice Path Enumeration: The Kernel Method; Gamma and Zeta Function; Harmonic Numbers and Their Generating Functions; Approximation of Binomial Coefficients; Mellin Transform and Asymptotics of Harmonic Sums; The Mellin-Perron Formula; Mellin-Perron Formula: Divide-and-Conquer Recursions ; Rice’s Method; Approximate Counting; Singularity Analysis of Generating Functions; Longest Runs in Words; Inversions in Permutations and Pumping Moments; Tree Function; The Saddle Point Method; Hwang’s Quasi-Power Theorem; ; TOPICS; ; Asymptotic Normality in Enumeration ; E. Rodney Canfield ; The Normal Distribution; Method 1: Direct Approach; Method 2: Negative Roots; Method 3: Moments; Method 4: Singularity Analysis; Local Limit Theorems; Multivariate Asymptotic Normality; Normality in Service to Approximate Enumeration; ; Trees ; Michael Drmota ; Introduction; Basic Notions; Generating Functions; Unlabeled Trees; Labeled Trees; Selected Topics on Trees; ; Planar maps ; Gilles Schaeffer ; What is a Map?; Counting Tree-Rooted Maps; Counting Planar Maps; Beyond Planar Maps, an Even Shorter Account; ; Graph Enumeration ; Marc Noy ; Introduction; Graph Decompositions; Connected Graphs with Given Excess; Regular Graphs; Monotone and Hereditary Classes; Planar Graphs; Graphs on Surfaces and Graph Minors; Digraphs; Unlabelled Graphs; ; Unimodality, Log-Concavity, Real–Rootedness and Beyond ; Petter Brándén ; Introduction; Probabilistic Consequences of Real–Rootedness; Unimodality and G-Nonnegativity; Log–Concavity and Matroids; Infinite Log-Concavity; The Neggers–Stanley Conjecture; Preserving Real–Rootedness; Common Interleavers; Multivariate Techniques; Historical Notes; ; Words; Dominique Perrin and Antonio Restivo ; Introduction; Preliminaries; Conjugacy; Lyndon words; Eulerian Graphs and De Bruijn Cycles; Unavoidable Sets; The Burrows-Wheeler Transform; The Gessel-Reutenauer Bijection; Suffix Arrays; ; Tilings ; James Propp; Introduction and Overview; The Transfer Matrix Method; Other Determinant Methods; Representation-Theoretic Methods; Other Combinatorial Methods; Related Topics, and an Attempt at History; Some Emergent Themes; Software; Frontiers; ; Lattice Path Enumeration ; Christian Krattenthaler; Introduction; Lattice Paths Without Restrictions; Linear Boundaries of Slope 1; Simple Paths with Linear Boundaries of Rational Slope, I; Simple Paths with Linear Boundaries with Rational Slope, II; Simple Paths with a Piecewise Linear Boundary; Simple Paths with General Boundaries; Elementary Results on Motzkin and Schroder Paths; A continued Fraction for the Weighted Counting of Motzkin Paths; Lattice Paths and Orthogonal Polynomials; Motzkin Paths in a Strip; Further Results for Lattice Paths in the Plane; Non-Intersecting Lattice Paths; Lattice Paths and Their Turns; Multidimensional Lattice Paths; Multidimensional Lattice Paths Bounded by a Hyperplane; Multidimensional Paths With a General Boundary; The Reflection Principle in Full Generality; Q-Counting Of Lattice Paths and Rogers–Ramanujan Identities; Self-Avoiding Walks; ; Catalan Paths and q; t-enumeration ; James Haglund ; Introduction to q-Analogues and Catalan Numbers; The q; t-Catalan Numbers; Parking Functions and the Hilbert Series; The q; t-Schrӧder Polynomial; Rational Catalan Combinatorics; ; Permutation Classes ; Vincent Vatter ; Introduction; Growth Rates of Principal Classes; Notions of Structure; The Set of All Growth Rates; ; Parking Functions ; Catherine H. Yan ; Introduction; Parking Functions and Labeled Trees; Many Faces of Parking Functions; Generalized Parking Functions; Parking Functions Associated with Graphs; Final Remarks; ; Standard Young Tableaux ; Ron Adin and Yuval Roichman; Introduction; Preliminaries; Formulas for Thin Shapes; Jeu de taquin and the RS Correspondence; Formulas for Classical Shapes; More Proofs of the Hook Length Formula; Formulas for Skew Strips; Truncated and Other Non-Classical Shapes; Rim Hook and Domino Tableaux; q-Enumeration; Counting Reduced Words; Appendix 1: Representation Theoretic Aspects; Appendix 2: Asymptotics and Probabilistic Aspects; ; Computer Algebra; Manuel Kauers ; Introduction; Computer Algebra Essentials; Counting Algorithms; Symbolic Summation; The Guess-and-Prove Paradigm; Index
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations
• Subjects: 511.62; Combinatorial analysis; Numeration
• Languages: English
• ISBNs: 9781482220865
• Related ISBNs: 9781482220858
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.