The Radon transform on \({\mathbb{Z}}^ k_ 2\)
The paper investigates the uniqueness of the discrete Radon transform in various particular cases. For example, if \(S_ n\) is the symmetric group on n letters, \(Y=\{\pi \in S_ n:\) \(d(id,\pi)\leq 1\}\) where d is the Cayley metric, it is proved that the Radon transform of a function \(f: S_ n\to {\mathbb{R}}\), given by \(f_ Y(x)=\sum_{y\in Y+x}f(y)\) is one to one if and only if \(n\in \{1,3,4,5,6,8,10,12\}\).
scientific article; zbMATH DE number 3929650