Do the Properties of an S-adic Representation Determine Factor Complexity?

Abstract : The S-adic conjecture postulates the existence of a condition C such that a sequence has linear complexity if and only if it is an S-adic sequence satisfying C for some finite set S of morphisms. We present an overview of the factor complexity of S-adic sequences and we give some examples that either illustrate some interesting properties, or that are counterexamples to what might seem to be a "good" condition C.
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Fabien Durand, Julien Leroy, Gwenaël Richomme. Do the Properties of an S-adic Representation Determine Factor Complexity?. Journal of Integer Sequences, University of Waterloo, 2013, 16 (2), pp.Art 13.2.6. ⟨lirmm-00797654⟩

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