On TDP permutations (Q1822609)

A permutation \(\sigma\) : \(i\mapsto a_ i\), \(0\leq i<n\) is called a TDP permutation if \(i-a_ i\not\equiv j-a_ j mod n\) for \(i\neq j\). It is easy to see that there exists a TDP permutation iff n is odd. \textit{C. Tompkins} [Proc. Symp. Appl. Math. 6, 195-211 (1956; Zbl 0071.122)] listed the number of TDP permutations for \(n\leq 11.\) In the paper under review the author gives a combinatorial method for finding all TDP permutations for \(n\leq 15\), and discusses a group- theoretic method for generating TDP permutations. For \(n>15\), the number of TDP permutations is estimated by applying probability methods.