A characterization of the periods of periodic points of 1-norm nonexpansive maps (Q1879033)

The authors characterize the set \(R(n)\) of minimal periods of periodic points of 1-norm nonexpansive maps \(f: \mathbb R^n\to \mathbb R^n\) by arithmetical and combinatorial constrains. They introduce the notion of a restricted admissible array on \(2n\) symbols and show that \(R(n)\) is precisely the set of possible periods of these arrays. By using this equality, they compute the set \(R(n)\) for \(1\leq n \leq 10\). They also show that the largest element of \(R(n)\) satisfies \(\log \Psi(n)\sim \sqrt{2n\log n}\).