Reducible sums and splittable sets (Q752056)

For \(a_i,n_i\in {\mathbb{N}}\), \(i=1,...,k\) set \(s=\sum^{k}_{i=1}a_i/n_i\). If \(s'=\sum^{k}_{i=1}a_i'/n_i\), \(0\leq a_i'\leq a_i\), then \(s'\) is called a subsum of s. Further, s is called reducible if a subsum \(s'=1\) exists. The set \(\{n_1,...,n_k\}\) is called splittable iff whenever s is an integer greater than 1, then \(s\) is reducible. - In the paper criteria for reducibility and examples of irreducible sums are given. Further, relations between nonsplittable sets and irreducible sums are studied.