International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 2, Pages 215-224
doi:10.1155/IJMMS.2005.215

k-complementing subsets of nonnegative integers

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.