Palindromic complexity of codings of rotations

Abstract

International audienceWe 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

Exchange of three intervals: Substitutions and palindromicity

“…The claim in item (c) is analogous to (a). Cases (b) and (d) are derived from (a) and (c) by the use of equivalence (9).…”

On Words with the Zero Palindromic Defect

“…-In [7], the authors show that words coding rotation on the unit circle with respect to partition consisting of two intervals are rich. -In [29], the authors show a connection of rich words with the Burrows-Wheeler transform.…”

“…Many classes of words with the defect zero have been found, for example Sturmian words, words coding symmetrical interval exchange and complementary symmetric Rote words (see [1,7,15]). …”

Palindromic closures using multiple antimorphisms

“…ω also correspond to the word t 3,4 . The authors of [5] study this phenomenon for the generalized pseudopalindromic word on the binary alphabet, where ∆ ∈ {0, 1} N and Θ ∈ {R, E} N .…”