An isomorphism between the \(p\)-adic integers and a ring associated with a tiling of \(N\)-space by permutohedra
type: Item
instance of: scholarly article
title: An isomorphism between the \(p\)-adic integers and a ring associated with a tiling of \(N\)-space by permutohedra
zbMATH Open document ID: 0805.52012
DOI: 10.1016/0166-218X(92)00186-P
author: Wei Z. Kitto
author: Andrew Vince
author: David C. Wilson
published in: Discrete Applied Mathematics
publication date: 1994-07-31T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 612421
zbMATH Keywords: isomorphism
zbMATH Keywords: \(p\)-adic integers
zbMATH Keywords: tilings of \(N\)-space
zbMATH Keywords: permutohedra
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 612421