Resumen de Computations on Sofic S-gap Shifts

D. Ahmadi Dastjerdi, S. Jangjoo

• Let S = {si ∈ N ∪ {0} : 0 ≤ si < si+1, i ∈ N} and X(S) the S-gap shift associated to S with entropy h(X(S)). Let fS(x) = 1 − 1 xsn+1 be the entropy function which will be vanished at 2h(X(S)). Suppose X(S) is sofic with adjacency matrix A and the characteristic polynomial χA. Then for some rational function QS, χA(x) = QS(x) fS(x). This QS will be explicitly determined. We will show that ζ (t) = 1 fS (t−1) or ζ (t) = 1 (1−t) fS (t−1) when |S| < ∞ or |S|=∞ respectively. Here ζ is the zeta function of X(S). We will also compute the Bowen–Franks groups of a sofic S-gap shift.