Properties of Generalized (r,s,t,u)-Numbers

Arithmetic Properties of Generalized Euler Numbers

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.

Some Asymptotic Properties of Generalized Fibonacci Numbers

1. INTRODUCTION Horadam [1] has generalized two theorems of Subba Rao [3] which deal with some asymptotic p r o p e r t i e s of Fibonacci numbers. Horadam defined a sequence {w (n 2) where a , a are the roots of x 2-P 21 x + P 2 2 = 0. We shall let 06 """ LX r\ r\ UO r\-| • Horadam established two theorems for {w n }: I. The number of terms of {w n } not exceeding N is asymptotic to log(Nd/(P ...

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...

Addition two generalized fuzzy numbers

Generalized chromatic numbers and additive hereditary properties of graphs

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let P and Q be additive hereditary properties of graphs. The generalized chromatic number χQ(P) is defined as follows: χQ(P) = n iff P ⊆ Qn but P 6⊆ Qn−1. We investigate the generalized chromatic numbers of the well-known properties of graphs Ik, Ok, Wk, Sk and Dk.