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

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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 GBTnin a natural way as a quotient ring of Z[x]. The ring GBTncan also be considered as the set of all finite sequences s0s1...sk, with si∈ GBTn{plus 45 degree rule}αGBTnfor 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 EGBTnis isomorphic as a ring to the (2n+1-1)-adic integers. © 1994.

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Kitto, W. Z., Vince, A., & Wilson, D. C. (1994). An isomorphism between the p-adic integers and a ring associated with a tiling of N-space by permutohedra. Discrete Applied Mathematics, 52(1), 39–51. https://doi.org/10.1016/0166-218X(92)00186-P

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