Affiliation:
1. University of the Philippines, Institute of Mathematics, Quezon City, Philippinen
Abstract
Abstract
In this paper, orbit colorings of a lattice Λ were considered, extending the idea of obtaining lattice colorings based on cosets of a sublattice. Given a subgroup S of finite index in the symmetry group G of the lattice Λ, if T(S) is the subgroup of translations in G and L is the sublattice of Λ determined by T(S), then a homomorphism f from N = N
G
(T(S)) to the subgroup S
C
of permutations of the cosets of L in Λ is defined. This homomorphism was used to obtain S-orbit colorings of Λ and the corresponding color group H and color fixing group K. Moreover, S ker f ≤ K ≤ H ≤ N.
Subject
Inorganic Chemistry,Condensed Matter Physics,General Materials Science
Cited by
1 articles.
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