Kettle, Neil,
King, Andy
(2006)
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Proof of New Implicational Relationships between Generalized Symmetries (appendix for journal paper).
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University of Kent, School of Computing, University of Kent, Canterbury, Kent, CT2 7NF, 11 pp.

## Abstract

This note provides proof of some new implicational relationships between generalized symmetries. These relationships are formulated in terms of twelve symmetry types. Six of these symmetries are denoted T<sub>n</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup> where the index n?[1,6] indicates that a specific co-factor equivalence property holds between the variables x<sub>i</sub> and x<sub>j</sub>. The other six symmetries are denoted neg T<sub>n</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup>, and indicate that one co-factor is equivalent to the negation of the other. The relationships that are specified take the form, if T<sub>p</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup> and T<sub>q</sub><sup>x<sub>j</sub>,x<sub>k</sub></sup> hold then T<sub>r</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup> holds where T<sub>p</sub>,T<sub>q</sub> and T<sub>r</sub> denote one of these twelve symmetry types.

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