The Sheffer group and the Riordan group

نویسندگان

  • Tian-Xiao He
  • Leetsch C. Hsu
  • Peter Jau-Shyong Shiue
چکیده

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs. AMS Subject Classification: 05A15, 11B73, 11B83, 13F25, 41A58

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Characterization of Riordan Arrays and Sheffer-type Polynomial Sequences

Here we present a characterization of Sheffer-type polynomial sequences based on the isomorphism between the Riordan group and Sheffer group and the sequence characterization of Riordan arrays. We also give several alternative forms of the characterization of the Riordan group, Sheffer group and their subgroups. Formulas for the computation of the generating functions of Riordan arrays and Shef...

متن کامل

Self - Inverse Sheffer Sequences and Riordan

In this short note we focus on self-inverse Sheffer sequences and involutions in the Riordan group. We translate the results of Brown and Kuczma on self-inverse sequences of Sheffer polynomials to describe all involutions in the Riordan group.

متن کامل

Generalized Riordan arrays

In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to cn is an infinite, lower triangular array determined by the pair (g(t), f(t)) and has the generic element dn,k = [t/cn]g(t)(f(t))/ck, where cn is a fixed sequence of non-zero constants with c0 = 1. We demonstrate that the generalized Riordan arrays have similar properties to those of the class...

متن کامل

Riordan Arrays Associated with Laurent Series and Generalized Sheffer-Type Groups

A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, an...

متن کامل

Riordan Arrays, Sheffer Sequences and “Orthogonal” Polynomials

Riordan group concepts are combined with the basic properties of convolution families of polynomials and Sheffer sequences, to establish a duality law, canonical forms ρ(n,m) = ( n m ) cFn−m(m), c 6= 0, and extensions ρ(x, x − k) = (−1) xcFk(x), where the Fk(x) are polynomials in x, holding for each ρ(n,m) in a Riordan array. Examples ρ(n,m) = ( n m ) Sk(x) are given, in which the Sk(x) are “or...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 155  شماره 

صفحات  -

تاریخ انتشار 2007