Additive permutations with repeated elements (Q2715940)

The paper studies the concept of a \(RA\)-basis that generalizes additive permutations. It is a multiset \(X=(x_1, x_2, \ldots , x_k)\) of relatively prime integers such that, for some permutation \(Y\) of \(X\), the vector sum \(X+Y\) is again a permutation of \(X\). \(Y\) is called an \(R\)-additive permutation of \(X\). Example: \(X=(-1,0,0,1)\) and \(Y=(0,1,0,-1)\). Exercise: always \(\sum x_i=0\). Examples of families of \(RA\)-bases and bounds on the numbers of their \(R\)-additive permutations are given. Bases with \(k\leq 6\) and their additive permutations are completely determined.