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On strong shift equivalence over a Boolean semiring

Published online by Cambridge University Press:  19 September 2008

Ki Hang Kim  and
Fred W. Roush
Ki Hang Kim
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, Alabama 36195, USA
Fred W. Roush
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, Alabama 36195, USA
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Abstract

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Shift equivalence is the relation between A, B that there exists S, R, n > 0 with RA = BR, AS = SB, SR = An, RS = Bn. Strong shift equivalence is the equivalence relation generated by these equations with n = 1. We prove that for many Boolean matrices strong shift equivalence is characterized by shift equivalence and a trace condition. However, we also show that if A is strongly shift equivalent to B, then there exists a homomorphism from an iterated directed edge graph of A to the graph of B preserving the traces of powers. This yields results on colourings of iterated directed edge graphs and might distinguish new strong equivalence classes.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 81 - 97
Copyright
Copyright © Cambridge University Press 1986

References

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