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• W2017398076 abstract "The palindromization map $psi$ in a free monoid $A^*$ was introduced in 1997 by the first author in the case of a binary alphabet $A$, and later extended by other authors to arbitrary alphabets. Acting on infinite words, $psi$ generates the class of standard episturmian words, including standard Arnoux-Rauzy words. In this paper we generalize the palindromization map, starting with a given code $X$ over $A$. The new map $psi_X$ maps $X^*$ to the set $PAL$ of palindromes of $A^*$. In this way some properties of $psi$ are lost and some are saved in a weak form. When $X$ has a finite deciphering delay one can extend $psi_X$ to $X^{omega}$, generating a class of infinite words much wider than standard episturmian words. For a finite and maximal code $X$ over $A$, we give a suitable generalization of standard Arnoux-Rauzy words, called $X$-AR words. We prove that any $X$-AR word is a morphic image of a standard Arnoux-Rauzy word and we determine some suitable linear lower and upper bounds to its factor complexity. For any code $X$ we say that $psi_X$ is conservative when $psi_X(X^{*})subseteq X^{*}$. We study conservative maps $psi_X$ and conditions on $X$ assuring that $psi_X$ is conservative. We also investigate the special case of morphic-conservative maps $psi_{X}$, i.e., maps such that $phicirc psi = psi_Xcirc phi$ for an injective morphism $phi$. Finally, we generalize $psi_X$ by replacing palindromic closure with $theta$-palindromic closure, where $theta$ is any involutory antimorphism of $A^*$. This yields an extension of the class of $theta$-standard words introduced by the authors in 2006." @default.
• W2017398076 created "2016-06-24" @default.
• W2017398076 creator A5049480085 @default.
• W2017398076 date "2012-10-01" @default.
• W2017398076 modified "2023-09-29" @default.
• W2017398076 title "A generalized palindromization map in free monoids" @default.
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• W2017398076 doi "https://doi.org/10.1016/j.tcs.2012.01.029" @default.
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