Decidability, arithmetic subsequences and eigenvalues of morphic subshifts
F Durand, V Goyheneche - Bulletin of the Belgian Mathematical …, 2019 - projecteuclid.org
F Durand, V Goyheneche
Bulletin of the Belgian Mathematical Society-Simon Stevin, 2019•projecteuclid.orgWe prove decidability results on the existence of constant subsequences of uniformly
recurrent morphic sequences along arithmetic progressions. We use spectral properties of
the subshifts they generate to give a first algorithm deciding whether, given $ p\in\mathbb
{N} $, there exists such a constant subsequence along an arithmetic progression of common
difference $ p $. In the special case of uniformly recurrent automatic sequences we explicitly
describe the sets of such $ p $ by means of automata.
recurrent morphic sequences along arithmetic progressions. We use spectral properties of
the subshifts they generate to give a first algorithm deciding whether, given $ p\in\mathbb
{N} $, there exists such a constant subsequence along an arithmetic progression of common
difference $ p $. In the special case of uniformly recurrent automatic sequences we explicitly
describe the sets of such $ p $ by means of automata.
We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding whether, given , there exists such a constant subsequence along an arithmetic progression of common difference . In the special case of uniformly recurrent automatic sequences we explicitly describe the sets of such by means of automata.