2009/04/03 by Yunbao Huang, Huang, Yunbao · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #68R15 #Algorithms and Data Compression #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #math.CO #msc:68R15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0904.0562
28 pages
openalex publication_date 2009/04/03 · arxiv created 2011/08/09 · arxiv updated 2011/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Carpi (1993) and Lepisto (1994) proved independently that smooth words are cube-free for the alphabet 1, 2, but nothing is known on whether for the other 2-letter alphabets, smooth words are k-power-free for some suitable positive integer k. In this paper, we first establish the derivative formula of the concatenation of two smooth words and power derivative formula of smooth words over arbitrary 2-letter alphabets. Then by making use of power derivative formula, for arbitrary 2-letter alphabet a, b with a, b being positive integers and a<b, we prove that smooth words are (b+1)-power-free except for a=1 and b=3; and smooth words are quintic-free and there are infinitely many smooth biquadrates for the alphabet 1, 3. Moreover, we give the number of smooth words of form wn with a and b having the same parity.