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Balanced Strong Shift Equivalence, Balanced In-splits, and Eventual Conjugacy by Brix, Kevin Aguyar is a scholarly article available to read on EtoBox.

What is Balanced Strong Shift Equivalence, Balanced In-splits, and Eventual Conjugacy about?

We introduce the notion of balanced strong shift equivalence between square nonnegative integer matrices, and show that two finite graphs with no sinks are one-sided eventually conjugate if and only if their adjacency matrices are conjugate to balanced strong shift equivalent matrices. Moreover, we show that such graphs are eventually conjugate if and only if one can be reached by the other via a sequence of out-splits and balanced in-splits; the latter move being a variation of the classical in-split move introduced by Williams in his study of shifts of finite type. We also relate one-sided eventual conjugacies to certain block maps on the finite paths of the graphs. These characterizations emphasize that eventual conjugacy is the one-sided analog of two-sided conjugacy.

Author

Brix, Kevin Aguyar

Published

2019

Language

EN