\(k\)-complementing subsets of nonnegative integers (Q2570001)

Summary: A collection \(\{S_1, S_2,\dots\}\) 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 \(S_1, S_2, \dots\). 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.