Lower bounds for sumsets of multisets in Z_p^2
Number Theory
2012-09-03 v3
Abstract
The classical Cauchy-Davenport theorem implies the lower bound n+1 for the number of distinct subsums that can be formed from a sequence of n elements of the cyclic group Z_p (when p is prime and n<p). We generalize this theorem to a conjecture for the minimum number of distinct subsums that can be formed from elements of a multiset in (Z_p)^m; the conjecture is expected to be valid for multisets that are not "wasteful" by having too many elements in nontrivial subgroups. We prove this conjecture in (Z_p)^2 for multisets of size p+k, when k is not too large in terms of p.
Keywords
Cite
@article{arxiv.1107.4392,
title = {Lower bounds for sumsets of multisets in Z_p^2},
author = {Greg Martin and Alexis Peilloux and Erick B. Wong},
journal= {arXiv preprint arXiv:1107.4392},
year = {2012}
}
Comments
13 pages. The quantitative bound in Theorem 1.8 has been improved, and a new coauthor has been added. These statements are not unrelated