A Spanning Tree Invariant for Markov Shifts

  title={A Spanning Tree Invariant for Markov Shifts},
  author={Selim Tuncel},
We introduce a new type of invariant of block isomorphism for Markov shifts, defined by summing the weights of all spanning trees for a presentation of the Markov shift. We give two proofs of invariance. The first uses the Matrix-Tree Theorem to show that this invariant can be computed from a known invariant, the stochastic zeta function of the shift. The second uses directly the definition to show invariance under state splitting, from which all block isomorphisms can be built. 

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