Lattice path combinatorics and applications. (2019)

• Record Type: Book
• Further Information: Note: George E. Andrews, Christian Krattenthaler, Alan Krinik, editors.
• Editors: Andrews, George E, 1938-; Krattenthaler, C (Christian), 1958-; Krinik, Alan C (Alan Cary)
• Other Names: International Conference on Lattice Path Combinatorics and Applications, 8th
• Contents: Intro; Foreword; Lattice Path Conference: A Journey; Preface; Program Schedule; 8th International Conference on Lattice Path Combinatorics and Applications; Contents; Contributors; Professor Lajos Takács: A Tribute; 1 In Memory of Lajos Takács; 1.1 How Did I Come to Know Takács?; 1.2 Left the USA, Back to Iran; 1.3 At Case Western Reserve University; 1.4 Left the USA, Back to Iran Again!; 1.5 Meeting Professor Mohanty in Canada; 1.6 Back to the USA and Started a Lifelong Living!; 1.7 Remembrances; 2 The Life of Lajos Takács; 2.1 A Biographical Sketch of Lajos Takács 3 Collaboration with AndrewsReferences; A Refinement of the Alladi-Schur Theorem; 1 Introduction; 2 Proof of Theorem 5.2; 3 Conclusion; References; Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method; 1 Introduction; 2 The General Setup and Some Preliminaries; 3 (Old-time) Basketball Walks: Steps mathcalS={-2, -1, +1, +2}; 3.1 Generating Functions for Positive (Old-time) Basketball Walks: The Kernel Method; 3.2 How to Get a Closed Form for Coefficients: Lagrange-Bürmann Inversion; 3.3 How to Derive the Corresponding Asymptotics: Singularity Analysis 4 General Case: Lattice Walks with Arbitrary Steps4.1 Counting Walks with Steps in mathcalS={0, pm1, …, pmh}; 4.2 Counting Walks with Steps in mathcalS={pm1, …, pmh}; 5 Some Links with Other Combinatorial Problems; 5.1 Trees and Basketball Walks from 0 to 1; 5.2 Increasing Trees and Basketball Walks; 5.3 Boolean Trees and Basketball Walks from 0 to 2; 6 Conclusion; References; The Kernel Method for Lattice Paths Below a Line of Rational Slope; 1 Introduction; 2 Trees, Fractional Trees, Imaginary Trees; 3 Knuth's AofA Problem #4; 4 A Bijection for Lattice Paths Below a Rational Slope 5 Functional Equation and Closed-Form Expressions for Lattice Paths of Slope 2/56 Asymptotics; 7 Links with the Work of Nakamigawa and Tokushige; 8 Duchon's Club and Other Slopes; 8.1 Duchon's Club: Slope 2/3 and Slope 3/2; 8.2 Arbitrary Rational Slope; 9 Conclusion; References; Enumeration of Colored Dyck Paths Via Partial Bell Polynomials; 1 Introduction; 2 Enumeration of Colored Dyck Words; 3 Representation in Terms of Partial Bell Polynomials; 4 Examples; References; A Review of the Basic Discrete q-Distributions; 1 Introduction; 2 Basic q-Combinatorics and q-Hypergeometric Series
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource (xxv, 418 pages), illustrations (some color)
• Subjects: 511.3/3; Lattice paths -- Congresses; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030111021; 3030111024
• Related ISBNs: 9783030111014
• Notes: Note: Online resource; title from PDF title page (SpringerLink, viewed March 5, 2019).
• 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.