A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Automatic sequences based on Parry or Bertrand numeration systems




Julkaisun tekijät: Massuir Adeline, Peltomäki Jarkko, Rigo Michel
Kustantaja: Elsevier
Julkaisuvuosi: 2019
Journal: Advances in Applied Mathematics
Volyymi: 108

Tiivistelmä

We study the factor complexity and closure properties of automatic
sequences based on Parry or Bertrand numeration systems. These automatic
sequences can be viewed as generalizations of the more typical $k$-automatic sequences and Pisot-automatic sequences. We show that, like $k$-automatic
sequences, Parry-automatic sequences have sublinear factor complexity
while there exist Bertrand-automatic sequences with superlinear factor
complexity. We prove that the set of Parry-automatic sequences with
respect to a fixed Parry numeration system is not closed under taking
images by uniform substitutions or periodic deletion of letters. These
closure properties hold for $k$-automatic sequences and
Pisot-automatic sequences, so our result shows that these properties are
lost when generalizing to Parry numeration systems and beyond.
Moreover, we show that a multidimensional sequence is $U$-automatic with respect to a positional numeration system $U$ with regular language of numeration if and only if its $U$-kernel is finite.



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Last updated on 2019-21-08 at 22:33