86 research outputs found
Relation between powers of factors and recurrence function characterizing Sturmian words
In this paper we use the relation of the index of an infinite aperiodic word
and its recurrence function to give another characterization of Sturmian words.
As a byproduct, we give a new proof of theorem describing the index of a
Sturmian word in terms of the continued fraction expansion of its slope. This
theorem was independently proved by Carpi and de Luca, and Damanik and Lenz.Comment: 11 page
Self-Matching Properties of Beatty Sequences
We study the selfmatching properties of Beatty sequences, in particular of
the graph of the function against for every
quadratic unit . We show that translation in the argument by an
element of generalized Fibonacci sequence causes almost always the
translation of the value of function by . More precisely, for fixed
, we have , where . We determine the set of
mismatches and show that it has a low frequency, namely .Comment: 7 page
Integers in number systems with positive and negative quadratic Pisot base
We consider numeration systems with base and , for quadratic
Pisot numbers and focus on comparing the combinatorial structure of the
sets and of numbers with integer expansion in base
, resp. . Our main result is the comparison of languages of
infinite words and coding the ordering of distances
between consecutive - and -integers. It turns out that for a
class of roots of , the languages coincide, while for other
quadratic Pisot numbers the language of can be identified only with
the language of a morphic image of . We also study the group
structure of -integers.Comment: 19 pages, 5 figure
Factor versus palindromic complexity of uniformly recurrent infinite words
We study the relation between the palindromic and factor complexity of
infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1)
\leq \Delta C(n) + 2, for all n \in N. For a large class of words it is a
better estimate of the palindromic complexity in terms of the factor complexity
then the one presented by Allouche et al. We provide several examples of
infinite words for which our estimate reaches its upper bound. In particular,
we derive an explicit prescription for the palindromic complexity of infinite
words coding r-interval exchange transformations. If the permutation \pi
connected with the transformation is given by \pi(k)=r+1-k for all k, then
there is exactly one palindrome of every even length, and exactly r palindromes
of every odd length.Comment: 16 pages, submitted to Theoretical Computer Scienc
Number representation using generalized -transformation
We study non-standard number systems with negative base . Instead of
the Ito-Sadahiro definition, based on the transformation of the
interval into itself, we
suggest a generalization using an interval with . Such
generalization may eliminate certain disadvantages of the Ito-Sadahiro system.
We focus on the description of admissible digit strings and their periodicity.Comment: 22 page
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