Palindromic complexity of codings of rotations

Alexandre Blondin Masse (1) , Srečko Brlek (2) , Sébastien Labbé (3) , Laurent Vuillon (4)

1 Laboratoire de Mathématiques
2 Département d'informatique [Montréal]
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
4 LAMA - Laboratoire de Mathématiques

We study the palindromic complexity of infinite words obtained by coding rotations on partitions of the unit circle by inspecting the return words. The main result is that every coding of rotations on two intervals is full, that is, it realizes the maximal palindromic complexity. As a byproduct, a slight improvement about return words in codings of rotations is obtained: every factor of a coding of rotations on two intervals has at most 4 complete return words, where the bound is realized only for a finite number of factors. We also provide a combinatorial proof for the special case of complementary-symmetric Rote sequences by considering both palindromes and antipalindromes occurring in it.

Domaines: Mathématique discrète [cs.DM]

Alexandre Blondin Masse, Srečko Brlek, Sébastien Labbé, Laurent Vuillon. Palindromic complexity of codings of rotations. Theoretical Computer Science, 2011, 412 (46), pp.6455-6463. ⟨10.1016/j.tcs.2011.08.007⟩. ⟨hal-00939195⟩