Two q-Analogues of Poly-Stirling Numbers

نویسنده

  • Brian K. Miceli
چکیده

We develop two q-analogues of the previously defined poly-Stirling numbers of the first and second kinds. We also develop the corresponding q-rook theory models to give combinatorial interpretations to these numbers.

برای دانلود رایگان 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

q-Analogues of multiparameter non-central Stirling and generalized harmonic numbers

Keywords: Stirling numbers q-Stirling numbers Multiparameter non-central Stirling numbers Comtet numbers q-Analogue Harmonic numbers Generalized q-harmonic numbers a b s t r a c t In this paper we derive q-analogues of the multiparameter non-central Stirling numbers of the first and second kind, introduced by El-Desouky. Moreover, recurrence relations, explicit formulas and a connection between...

متن کامل

Rook Theory, Generalized Stirling Numbers and (p, q)-Analogues

In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p, q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We al...

متن کامل

Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

متن کامل

A Rook Theory Model for the Generalized p, q-Stirling Numbers of the First and Second Kind

In (EJC 11 (2004), #R84), Remmel and Wachs presented two natural ways to define p, qanalogues of the generalized Stirling numbers of the first and second kind, S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue (Adv. App. Math 20 (1998), 366-384). In this paper, we present a rook theoretic model for each type of p, q-analogue based on a pair of boards parametrized by the nonnegative integ...

متن کامل

Elliptic Rook and File Numbers

Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel’s q-rook numbers by two additional independent parameters a and b, and a nome p. The elliptic rook numbers are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and ...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011