ExampleOfANonStutteringWordOfSmallComplexity < Substitutions

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Substitutions.ExampleOfANonStutteringWordOfSmallComplexityr1.1 - 15 Jun 2007 - 23:58 - ThierryMonteiltopic end

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Example of a non stuttering word of small complexity

Definition

The word is given in a S-adic way :

$x = x_0 = \sigma_0 \circ \sigma_1 \circ \sigma_2 \circ \dots (0)$
$x_k=\sigma_k \circ \sigma_{k+1} \circ \sigma_{k+2} \circ \dots (0) = \sigma_k(x_{k+1})$

where

$\sigma_k : A_{k+1} \to A_k = \{0,\dots,\alpha_k-1 \}$
$\sigma_k(i) = 01234\dots (\alpha_k-1) 0^i$

Bispecials of :

shorts :
longs : $0^j\sigma_k(v)01234\dots0^i$ where is a bispecial of $x_{k+1}$

Multiplicities

to be continued...

Historical context

Sabotage de la theorie de Boris big grin

A word x is said to be stuttering if, when O_n stands for the first position in x where a factor of length n appears for the second time, then O_n / n converges to infinity. This example provided by Julien Cassaigne gives a non-stuttering word of small complexity.
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Substitutions.ExampleOfANonStutteringWordOfSmallComplexity moved from Substitutions.ExampleOfANonStutteringWord on 15 Jun 2007 - 23:59 by ThierryMonteil - put it back

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