Sciweavers

Share
IANDC
2007

Exponential lower bounds for the number of words of uniform length avoiding a pattern

9 years 2 months ago
Exponential lower bounds for the number of words of uniform length avoiding a pattern
We study words on a finite alphabet avoiding a finite collection of patterns. Given a pattern p in which every letter that occurs in p occurs at least twice, we show that the number of words of length n on a finite alphabet that avoid p grows exponentially with n as long as the alphabet has at least 4 letters. Moreover, we give lower bounds describing this exponential growth in terms of the size of the alphabet and the number of letters occurring in p. We also obtain analogous results for the number of words avoiding a finite collection of patterns. We conclude by giving some questions. Key words: pattern avoidance, combinatorics on words, avoidable patterns.
Jason P. Bell, Teow Lim Goh
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2007
Where IANDC
Authors Jason P. Bell, Teow Lim Goh
Comments (0)
books