A note on the complexity of C∞-words

Authors:
Yun Bao Huang;William D. Weakley
Affiliations:
Department of Mathematics, Hangzhou Normal University, Xiasha Economic Development Area, Hangzhou, Zhejiang 310036, China;Department of Mathematical Sciences, Indiana - Purdue University at Fort Wayne, Fort Wayne, IN 46805, USA
Venue:
Theoretical Computer Science
Year:
2010

Citing 5
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Abstract

Let @c(n) be the number of C^~-words of length n. Say that a C^~-word w is left doubly extendable (LDE) if both 1w and 2w are C^~. We show that for any positive real number @f and positive integer N such that the proportion of 2's is greater than 12-@f in each LDE word of length exceeding N, there are positive constants c"1 and c"2 such that c"1n^l^o^g^3^l^o^g^(^(^3^/^2^)^+^@f^+^(^2^/^N^)^)