A Combinatorial Formula for the Linearization Coefficients of General Sheffer Polynomials
نویسندگان
چکیده
We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and MeixnerPollaczek polynomials. Furthermore, we give a new and explicit real version of the corresponding formula for Meixner-Pollaczek polynomials. Our proof is based on some explicit bijections and sign-reversing weight-preserving involutions. Running head: Combinatorics of Sheffer polynomials
منابع مشابه
Weighted Derangements and the Linearization Coefficients of Orthogonal Sheffer Polynomials
The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical exp...
متن کاملAppell Polynomials and Their Relatives
This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...
متن کاملA Deterministic Multiple Key Space Scheme for Wireless Sensor Networks via Combinatorial Designs
The establishing of a pairwise key between two nodes for encryption in a wireless sensor network is a challenging issue. To do this, we propose a new deterministic key pre-distribution scheme which has modified the multiple key space scheme (MKSS). In the MKSS, the authors define two random parameters to make better resilience than existing schemes. Instead of a random selection of these parame...
متن کاملLinearization Coefficients for the Jacobi Polynomials
i P (α,β) ni (x) et en déduire une évaluation dans le cas particulier où n1 = n2 + · · ·+ nm. ABSTRACT. — The explicit non-negative representation of the linearization coefficients of the Jacobi polynomials obtained by RAHMAN seems to be difficult to be derived by combinatorial methods. However several combinatorial interpretations can be provided for the integral of the product of Jacobi polyn...
متن کاملLinearization coefficients for orthogonal polynomials using stochastic processes
ABSTRACT. Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical families of orthogonal polynomials. Starting with a stochastic process and using the stochastic measures machinery introduced by Rota and Wallstrom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2001