LEADER 03696nam 2200517 450 001 9910568247803321 005 20231110214921.0 010 $a3-030-94151-5 035 $a(MiAaPQ)EBC6965070 035 $a(Au-PeEL)EBL6965070 035 $a(CKB)21707968800041 035 $a(PPN)262167816 035 $a(EXLCZ)9921707968800041 100 $a20221123d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 04$aThe Riordan group and applications /$fLouis Shapiro [and six others] 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2022] 210 4$d©2022 215 $a1 online resource (376 pages) 225 1 $aSpringer Monographs in Mathematics 311 08$aPrint version: Shapiro, Louis The Riordan Group and Applications Cham : Springer International Publishing AG,c2022 9783030941505 327 $aIntro -- 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. 327 $a9.4 Combinatorial Polynomials as Moments of Riordan Arrays -- 9.5 Continued Fractions and Riordan Arrays -- Exercises -- References -- Appendix Solutions -- References -- Index. 410 0$aSpringer Monographs in Mathematics 606 $aCombinatorial analysis 606 $aCombinatorial analysis$xData processing 606 $aMatemàtica discreta$2thub 606 $aAnàlisi combinatòria$2thub 608 $aLlibres electrònics$2thub 615 0$aCombinatorial analysis. 615 0$aCombinatorial analysis$xData processing. 615 7$aMatemàtica discreta 615 7$aAnàlisi combinatòria 676 $a511.6 702 $aShapiro$b Louis$f1941- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910568247803321 996 $aThe Riordan group and applications$92966297 997 $aUNINA