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Smooth words on 2-letter alphabets having same parity

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Smooth words on 2-letter alphabets having same parity
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). Key words: Smooth words, Kolakoski word, Lyndon factorization, letter frequency
Srecko Brlek, Damien Jamet, Geneviève Paqui
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Srecko Brlek, Damien Jamet, Geneviève Paquin
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