Copyright © 2005 Hindawi Publishing Corporation. 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

A collection {S1,S2,…} of nonempty sets is called a complementing system of subsets for a set X of nonnegative integers if every element of X can be uniquely expressed as a sum of elements of the sets S1,S2,… We present a complete characterization of all complementing systems of subsets for the set of the first n nonnegative integers as well as an explicit enumeration formula.