The Riordan group and applications / / Louis Shapiro [and six others]

• Record Nr.: UNINA9910568247803321
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer International Publishing, , [2022]; ©2022
• ISBN: 3-030-94151-5
• Descrizione fisica: 1 online resource (376 pages)
• Collana: Springer Monographs in Mathematics
• Disciplina: 511.6
• Soggetti: Combinatorial analysis; Combinatorial analysis - Data processing; Matemàtica discreta; Anàlisi combinatòria; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Foreword -- Preface -- Part I: Lou Shapiro's -- Part II: Renzo Sprugnoli's -- Part III: Overview of the book -- Acknowledgements -- Contents -- Notation -- 1 Introduction -- 1.1 What are Riordan Arrays? -- 1.2 Origins and Motivation -- 1.3 Elementary Applications -- Exercises -- References -- 2 Extraction of Coefficients and Generating Functions -- 2.1 Formal Power Series -- 2.2 Coefficient Extraction -- 2.3 Lagrange Inversion Theorem -- 2.4 Generating Functions -- Exercises -- References -- 3 The Riordan Group -- 3.1 Riordan Arrays and the Riordan Group -- 3.2 Some Special Subgroups -- 3.3 Several Aspects of the Riordan Group -- Exercises -- References -- 4 Characterization of Riordan Arrays by Special Sequences -- 4.1 The A- and Z- Sequences -- 4.2 The A-matrix -- 4.3 Is It a Riordan Array? -- Exercises -- References -- 5 Combinatorial Sums and Inversions -- 5.1 Combinatorial Sums -- 5.2 Combinatorial Inversions -- Exercises -- References -- 6 Generalized Riordan Arrays -- 6.1 Exponential Riordan Arrays -- 6.2 Generalized Riordan Arrays and the Riordan Group -- 6.3 Relations Between Riordan Arrays and Sheffer Sequences -- 6.4 Special Riordan Arrays and Sheffer Sequences -- 6.5 Double Riordan Arrays and Sheffer Polynomial Pairs -- References -- 7 Extensions of the ; Riordan Group -- 7.1 Three-Dimensional Riordan Group -- 7.2 Three-Dimensional Riordan Arrays -- 7.3 The Riordan Group in Several Variables -- Exercises -- References -- 8 q-Analogs of Riordan Arrays -- 8.1 Combinatorial q-Analogs -- 8.2 Eulerian Generating Functions -- 8.3 q-Riordan Arrays -- 8.4 Combinatorial Applications of the q-Riordan Arrays -- References -- 9 Orthogonal Polynomials -- 9.1 Orthogonal Polynomials and Riordan Arrays -- 9.2 Exponential Riordan Arrays and Classical Orthogonal Polynomials -- 9.3 Orthogonal Polynomials as Moments.; 9.4 Combinatorial Polynomials as Moments of Riordan Arrays -- 9.5 Continued Fractions and Riordan Arrays -- Exercises -- References -- Appendix Solutions -- References -- Index.