252 research outputs found
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
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
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