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Smooth words on 2-letter alphabets having same parity

机译:具有相同奇偶校验的2个字母的单词平滑

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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 are 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){sup}(1/2) + 1).
机译:在本文中,我们考虑2个字母的字母表{a,b}上的平滑词,其中a,b是具有相同奇偶校验的整数,0

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