03694nam 2200517 450 99647203660331620231110214921.03-030-94151-5(MiAaPQ)EBC6965070(Au-PeEL)EBL6965070(CKB)21707968800041(PPN)262167816(EXLCZ)992170796880004120221123d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Riordan group and applications /Louis Shapiro [and six others]Cham, Switzerland :Springer International Publishing,[2022]©20221 online resource (376 pages)Springer Monographs in Mathematics Print version: Shapiro, Louis The Riordan Group and Applications Cham : Springer International Publishing AG,c2022 9783030941505 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.Springer Monographs in Mathematics Combinatorial analysisCombinatorial analysisData processingMatemàtica discretathubAnàlisi combinatòriathubLlibres electrònicsthubCombinatorial analysis.Combinatorial analysisData processing.Matemàtica discretaAnàlisi combinatòria511.6Shapiro Louis1941-MiAaPQMiAaPQMiAaPQBOOK996472036603316The Riordan group and applications2966297UNISA