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
Department of Mathematics, University of Lagos, Akoka-Yaba, Lagos 101017, Nigeria
Received 9 September 2004
Copyright © 2005 Augustine O. Munagi. 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.