$\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts

Abstract

We prove that the multivariate zeta function of a sofic-Dyck shift is the commutative series of some visibly pushdown language. As a consequence the zeta function of a sofic-Dyck shift is the generating function of a visibly pushdown language and is thus an $\mathbb{N}$-algebraic series.

arXiv commentThis paper has been withdrawn by the authors due to an error in the proof of the main result

References in corpus (2)

• The Zeta function, Periodic Points and Entropies of the Motzkin Shift
• Subshifts from sofic shifts and Dyck shifts, zeta functions and topological entropy