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Graded alphabets, circular codes, free Lie algebras and comma-free codes

Abstract : We show how the use of graded alphabets allows one to provide simpler proofs of some results on free monoids and free Lie algebras. We first generalize to graded alphabets the characterization of the length distributions of circular codes. We also show that the existence of a circular code with a given distribution of degrees is equivalent to the existence of an embedding of Lie algebras. We finally give a generalization to graded alphabets of the famous result of Eastman on comma free codes of odd degree.
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https://hal-upec-upem.archives-ouvertes.fr/hal-03134035
Contributor : Dominique Perrin <>
Submitted on : Monday, February 8, 2021 - 8:30:33 AM
Last modification on : Thursday, February 11, 2021 - 3:01:50 AM
Long-term archiving on: : Sunday, May 9, 2021 - 6:15:24 PM

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Dominique Perrin, Christophe Reutenauer. Graded alphabets, circular codes, free Lie algebras and comma-free codes. Discrete Mathematics, Elsevier, 2021. ⟨hal-03134035⟩

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