Generalized riordan arrays
WebBy using exponential Riordan array methods, we give some criteria for total positivity of the triangular matrix of coefficients of the generalized cycle index polynomials, the Toeplitz matrix and Hankel matrix of the polynomial sequence in terms of the exponential formula, the logarithmic formula, and the fractional formula, respectively. WebUsing the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invariant sequences that arise …
Generalized riordan arrays
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WebOct 2, 2024 · Abstract: We show that the Catalan-Schroeder convolution recurrences and their higher order generalizations can be solved using Riordan arrays and the Catalan … WebUsing Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turns out that Delannoy matrix, Pascal matrix, and Fibonacci matrix are all special cases of the ...
WebApr 12, 2024 · In 2004, T. Kim and D. Kim first introduce the degenerate harmonic numbers and polynomials, moreover, those numbers and polynomials have been studied by many authors. In this paper, by using the Riordan arrays and generating functions, we derive a series of new combinatorial identities with respect to the degenerate harmonic numbers … WebJun 15, 2014 · Riordan arrays are used extensively in many contexts as a combinatorial tool for solving enumeration problems such as lattice path counting problems. In this …
WebGeneralized Riordan Arrays. Louis Shapiro, Renzo Sprugnoli, Paul Barry, Gi-Sang Cheon, Tian-Xiao He, Donatella Merlini et al. Pages 123-212. Extensions of the Riordan Group. ... 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 ... WebNov 20, 2024 · We give several new characterizations of Riordan Arrays, the most important of which is: if {d n,k} n,k ∈ N is a lower triangular arraywhose generic element d n,k linearly depends on the elements in a well-defined though large area of the array, then {d n,k} n,k ∈ N is Riordan. We also provide some applications of these characterizations …
WebGeneralized Pascal matrices with non-negative elements form an infinite-dimensional vector space. The paper gives an idea of groups similar to the generalized Riordan groups, but associated with matrices, which in the space of generalized Pascal matrices correspond to the points at infinity; examples of such matrices are the matrix of q q ...
WebOct 22, 2016 · The theory of Riordan arrays studies the properties of formal power series and their sequences. The notion of generalized Lagrange series proposed in the present … command key for snipping toolWebOct 22, 2016 · The theory of Riordan arrays studies the properties of formal power series and their sequences. The notion of generalized Lagrange series proposed in the present paper is intended to fill the gap in the methodology of this theory. Generalized Lagrange series appear in it implicitly, as various equalities. No special notation is provided for … command key for redoWebJun 15, 2014 · Second, we extend this method to the generalized Riordan array with multiple support functions in order to deal with the transient analysis of M / M / 1 queue with non-zero customers at the initial point. Numerical examples are also given to show how easy and quick the transient probability obtained from the Riordan method can be computed. command key for macWebMay 14, 2024 · Abstract: In this paper, we generalize the results due to Luzon and Moron, and present a characterization of the generalized Riordan arrays. Using this characterization, we establish a recurrence for the generalized Sheffer sequences, and study some special types of polynomial sequences, including the generalized Lucas u … command key for downloadWebSep 16, 2024 · This paper is concerned with the combinatorial identities of the harmonic and the hyperharmonic Fibonacci numbers. By using the symmetric algorithm, we get some identities which improve the usual results and generalize known equations. Moreover, with the help of concept of Riordan array, we obtain the generating functions for these … command key hpWebGeneralized Riordan arrays: their time has come Generalized Riordan arrays are ubiquitous, but not always recognized in the literature. We should use them more systematically, as a unifying device. They fit into a much bigger picture of multivariate GF asymptotics, lattice paths, Lagrange inversion, and the kernel method. dry fried chilli beefWebWe use an algebraic approach to study the connection between generating trees and proper Riordan Arrays deriving a theorem that, under suitable conditions, associates a … command key laptop