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shapiro louis; sprugnoli renzo; barry paul; cheon gi-sang; he tian-xiao; merlini donatella; wang weiping - the riordan group and applications
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The Riordan Group and Applications

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 04/2023





Trama

The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field.  The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve asa text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.





Sommario

1  Introduction.- 2 Extraction of coefficients and generating functions.- 3 The Riordan group.- 4 Characterization of Riordan arrays by special sequences.- 5 Combinatorial sums and inversions.- 6 Generalized Riordan arrays.- 7  Extensions of the Riordan group.- 8 q-analogs of Riordan arrays.- 9 Orthogonal polynomials. Solutions.- Index.





Autore

Louis Shapiro is a Professor Emeritus at Howard University. He has taught at Howard for 56 years with research interests in enumerative combinatorics, finite groups, and of course the Riordan group. He is also an avid runner and square dance caller.

Renzo Sprugnoli is a mathematician and computer scientist working in the fields of analysis of algorithms and combinatorics. Of particular note his works on the computation of combinatorial sums and the enumeration of lattice paths through Riordan arrays and the special sequences arising in this context. As a full professor, he has taught classes on algorithms, data structures and databases at the University of Florence.

Paul Barry is Emeritus professor of mathematics at Waterford Institute of Technology, Ireland.  He carries out research into integer sequences and Riordan arrays. He is the author of the book Riordan Arrays: A Primer.

Gi-Sang Cheon is a mathematician working in the field of combinatorial matrix theory. He is a professor at the Department of Mathematics of Sungkyunkwan University in South Korea.

Tian-Xiao He is a professor of mathematics and the Earl and Marian A. Beling Professor of Natural Science at Illinois Wesleyan University. His research fields include enumerative combinatorics, Riordan group, numerical analysis, approximate theory, wavelet analysis, and number theory. 

Donatella Merlini is a computer scientist working in the fields of analysis of algorithms, enumerative combinatorics, symbolic computation and data mining, subjects she  teaches at the University of Florence. Since her PhD thesis, she has studied both the theoretical aspects of Riordan arrays and the applications in the context of algorithms and data structures analysis.

Weiping Wang is an associate professor of School of Science at ZhejiangSci-Tech University, China. His research fields include enumerative combinatorics, combinatorial algorithms, and special functions. His research topics are related to combinatorial sequences, combinatorial summations, and multiple zeta values.












Altre Informazioni

ISBN:

9783030941536

Condizione: Nuovo
Collana: Springer Monographs in Mathematics
Dimensioni: 235 x 155 mm
Formato: Brossura
Illustration Notes:XXII, 362 p. 19 illus., 6 illus. in color.
Pagine Arabe: 362
Pagine Romane: xxii


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