Zeta functions and topological entropy of the Markov-Dyck shifts

Abstract

The Markov-Dyck shifts arise from finite directed graphs. An expression for the zeta function of a Markov-Dyck shift is given. The derivation of this expression is based on a formula in Keller (G. Keller, {\it Circular codes, loop counting, and zeta-functions}, J. Combinatorial Theory {\bf 56} (1991), pp. 75--83). For a class of examples that includes the Fibonacci-Dyck shift the zeta functions and topological entropy ae determined.

12 pages, 1 figure

References in corpus (3)

• Graph inverse semigroups, groupoids and their C*-algebras
• The Zeta function, Periodic Points and Entropies of the Motzkin Shift
• Cuntz-Krieger algebras and a generalization of Catalan numbers

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• On extensions of subshifts by finite groups
• Markov-Dyck shifts, neutral periodic points and topological conjugacy
• On a class of highly symmetric Markov-Dyck shifts
• On the Markov-Dyck shifts of vertex type