InforLorV4, Main, Merge, bibRecord, 004648

Smooth Words on a 2-letter alphabets having same parity

Identifieur interne : 004648 ( Main/Merge ); précédent : 004647; suivant : 004649

Smooth Words on a 2-letter alphabets having same parity

Auteurs : Srecko Brlek [Canada] ; Damien Jamet [France] ; Geneviève Paquin [Canada]

Source :

Theoretical Computer Science [ 0304-3975 ] ; 2008.

RBID : Hal:hal-00579854

English descriptors

mix :
- Kolakoski word, Lyndon factorization, Smooth words, letter frequency.

Abstract

In this paper, we consider smooth words over 2-letter alphabets {a, b}, where a, b are integers having same parity, with 0 < a < b. We show that all are recurrent and that the closure of the set of factors under reversal holds for odd alphabets only. We provide a linear time algorithm computing the extremal words, w.r.t. lexicographic order. The minimal word is an infinite Lyndon word if and only if either a = 1 and b odd, or a, b are even. A connection is established between generalized Kolakoski words and maximal infinite smooth words over even 2-letter alphabets revealing new properties for some of the generalized Kolakoski words. Finally, the frequency of letters in extremal words is 1/2 for even alphabets, and for a = 1 with b odd, the frequency of b's is 1/(√2b − 1 + 1).

Url:

https://hal.archives-ouvertes.fr/hal-00579854

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Le document en format XML

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<front><div type="abstract" xml:lang="en">In this paper, we consider smooth words over 2-letter alphabets {a, b}, where a, b are integers having same parity, with 0 < a < b. We show that all are recurrent and that the closure of the set of factors under reversal holds for odd alphabets only. We provide a linear time algorithm computing the extremal words, w.r.t. lexicographic order. The minimal word is an infinite Lyndon word if and only if either a = 1 and b odd, or a, b are even. A connection is established between generalized Kolakoski words and maximal infinite smooth words over even 2-letter alphabets revealing new properties for some of the generalized Kolakoski words. Finally, the frequency of letters in extremal words is 1/2 for even alphabets, and for a = 1 with b odd, the frequency of b's is 1/(√2b − 1 + 1).</div>
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Smooth Words on a 2-letter alphabets having same parity

Smooth Words on a 2-letter alphabets having same parity

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri