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Factor Frequencies in Languages Invariant Under Symmetries Preserving Factor Frequencies
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L'ubomíra Balková
Published/Copyright:
October 2, 2012
Abstract.
The number of frequencies of factors of length 
in a recurrent aperiodic infinite word does not exceed
, where 
is the first difference of factor complexity, as shown by Boshernitzan. Pelantová together with the author derived a better upper bound for infinite words whose language is closed under reversal. In this paper, we further diminish the upper bound for uniformly recurrent infinite words whose language
is invariant under all elements of a finite group of symmetries and we prove the optimality of the obtained upper bound.
Received: 2011-12-03
Accepted: 2012-05-30
Published Online: 2012-10-02
Published in Print: 2012-10-01
© 2012 by Walter de Gruyter Berlin Boston
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- The Googol-th Bit of the Erdős–Borwein Constant
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- The (r1,...,rp)-Stirling Numbers of the Second Kind
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Articles in the same Issue
- Masthead
- Two-Color Babylon
- On Abelian and Additive Complexity in Infinite Words
- Approximations of Additive Squares in Infinite Words
- The Googol-th Bit of the Erdős–Borwein Constant
- Odd Repdigits to Small Bases Are Not Perfect
- Enumeration of the Degree Sequences of Line-Hamiltonian Multigraphs
- The Characteristic Sequence and p-Orderings of the Set of d-th Powers of Integers
- Van der Waerden's Theorem on Homothetic Copies of {1,1+s,1+s+t}
- Sum-Products Estimates with Several Sets and Applications
- The 2-Adic, Binary and Decimal Periods of 1/3k Approach Full Complexity for Increasing k
- A Proof of Catalan's Convolution Formula
- Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
- The Impossibility of Certain Types of Carmichael Numbers
- Integer Subsets with High Volume and Low Perimeter
- Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
- A Generalized Diagonal Wythoff Nim
- A Recursive Process Related to a Partizan Variation of Wythoff
- The (r1,...,rp)-Stirling Numbers of the Second Kind
- Factor Frequencies in Languages Invariant Under Symmetries Preserving Factor Frequencies
- On k-Lehmer Numbers
