Sequences of integers with missing quotients |
| |
Authors: | Yong-Gao Chen Hong-Xia Yang |
| |
Institution: | School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China |
| |
Abstract: | Let S be any set of natural numbers, and A be a given set of rational numbers. We say that S is an A-quotient-free set if x,y∈S implies y/x∉A. Let and , where the supremum is taken over all A-quotient-free sets S, and are the upper and lower asymptotic densities of S respectively. Let ρ(A)=supSδ(S), where the supremum is taken over all A-quotient-free sets S such that δ(S) exists. In this paper we study the properties of , and ρ(A). |
| |
Keywords: | Quotient-free set Asymptotic density |
本文献已被 ScienceDirect 等数据库收录! |
|