Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 979487, 4 pages
http://dx.doi.org/10.1155/2013/979487
Research Article

Partitions of Natural Numbers with the Intersection Not Empty

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, China

Received 14 May 2012; Accepted 19 July 2012

Academic Editors: A. Cossidente, M. Eliasi, L. Feng, and M. Gionfriddo

Copyright © 2013 Wen Yu and Min Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be the set of nonnegative integers. For a given set the representation functions , are defined as the number of solutions of the equation with condition , , respectively. In this paper, we prove that if and , then cannot hold for all sufficiently large integers where .