An isomorphism between the \(p\)-adic integers and a ring associated with a tiling of \(N\)-space by permutohedra
Let \(A^*_ n\) denote the dual of the classical \(n\)-dimensional root lattice. Its Dirichlet-Voronoi-cells tile Euclidean \(E^ n\) by permutohedra (e.g. hexagons in \(E^ 2\), truncated octahedra in \(E^ 3\)). The idea of the paper is to show the interplay between the geometry of tiling \(E^ n\) by permutohedra and the corresponding algebraic structure. In particular relations to \((2^{n+1} -1)\)-adic integers (with \(n+1\) and \(2^{n+1}-1\) relatively prime) are investigated.
scientific article; zbMATH DE number 612421
scientific article