On various restricted sumsets
Combinatorics
2007-05-23 v2 Number Theory
Abstract
For finite subsets A_1,...,A_n of a field, their sumset is given by {a_1+...+a_n: a_1 in A_1,...,a_n in A_n}. In this paper we study various restricted sumsets of A_1,...,A_n with restrictions of the following forms: a_i-a_j not in S_{ij}, or alpha_ia_i not=alpha_ja_j, or a_i+b_i not=a_j+b_j (mod m_{ij}). Furthermore, we gain an insight into relations among recent results on this area obtained in quite different ways.
Keywords
Cite
@article{arxiv.math/0410529,
title = {On various restricted sumsets},
author = {Zhi-Wei Sun and Yeong-Nan Yeh},
journal= {arXiv preprint arXiv:math/0410529},
year = {2007}
}
Comments
11 pages; final version for J. Number Theory