An isomorphism between the p-adic integers and a ring associated with a tiling of N-space by permutohedra

  • Kitto W
  • Vince A
  • Wilson D
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Abstract

The classical lattice A*n, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBTn in a natural way as a quotient ring of Z[x]. The ring GBTn can also be considered as the set of all finite sequences s0 s1...sk, with si ∈ GBTn{plus 45 degree rule}αGBTn for all i, where α is an appropriately chosen element in GBTn. The extended generalized balance ternary (EGBTn) ring consists of all such infinite sequences. A primary goal of this paper is to prove that if 2n+1-1 and n+1 are relatively prime, then EGBTn is isomorphic as a ring to the (2n+1-1)-adic integers. © 1994.

Author-supplied keywords

  • Hexagonal tilings
  • Isomorphism
  • p-adic integers

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Authors

  • Wei Z. Kitto

  • Andrew Vince

  • David C. Wilson

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