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Equivalence Systems on Sets of Binary Sequences
Author(s) -
Behrendt Gerhard
Publication year - 1991
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/23.3.219
Subject(s) - mathematics , equivalence relation , transitive relation , binary relation , isomorphism (crystallography) , invariant (physics) , equivalence (formal languages) , automorphism group , combinatorics , automorphism , binary number , discrete mathematics , preorder , arithmetic , chemistry , crystal structure , mathematical physics , crystallography
Let Seq be the set of binary sequences, and for i εN; let e i be the equivalence relation on Seq given by equality for all components with index less than i . Let X be a subset of Seq and G the group of all permutations of X which leave each equivalence relation e i invariant. We give necessary and sufficient conditions for G to be transitive on X . We also determine the number of isomorphism classes of systems ( X , E ) where X ⊆ Seq and E is the set of restrictions of all relations e i to X × X such that the automorphism group of the system is transitive.