Arithmetic Properties of Generalized Euler Numbers
نویسندگان
چکیده
The generalized Euler number En|k counts the number of permutations of {1, 2, . . . , n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k = 2. In this paper, we study divisibility properties of a q-analog of En|k. In particular, we generalize two theorems of Andrews and Gessel [3] about factors of the q-tangent numbers.
منابع مشابه
On generalized fuzzy numbers
This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...
متن کاملOn the structural properties for the cross product of fuzzy numbers with applications
In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...
متن کاملSome arithmetic properties of the q-Euler numbers and q-Salié numbers
For m > n ≥ 0 and 1 ≤ d ≤ m, it is shown that the q-Euler number E 2m (q) is congruent to q m−n E 2n (q) mod (1 + q d) if and only if m ≡ n mod d. The q-Salié number S 2n (q) is shown to be divisible by (1 + q 2r+1) ⌊ n 2r+1 ⌋ for any r ≥ 0. Furthermore, similar congruences for the generalized q-Euler numbers are also obtained, and some conjectures are formulated.
متن کاملOn Apéry Numbers and Generalized Central Trinomial Coefficients
, and E0, E1, E2, . . . are Euler numbers. We show that the arithmetic means 1 n ∑n−1 k=0 (2k+1)Ak (n = 1, 2, 3, . . . ) are always integers and conjecture that ∑n−1 k=0 (2k+1)(−1) Ak ≡ 0 (mod n) for every n = 1, 2, 3, . . . . We also investigated generalized central trinomial coefficient Tn(b, c) (with b, c ∈ Z) which is the coefficient of xn in the expansion of (x2 + bx+ c)n. For any positive...
متن کاملViewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
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:
دوره شماره
صفحات -
تاریخ انتشار 1996