Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 17.3.2009 |
| Speaker: | Edita Pelantová, FJFI, České vysoké učení technické v Praze |
| Title: | Enumeration of factors of infinite words coding exchange of three intervals |
| Abstract: | (spoluautoři: P. Ambrož, A. Frid, Z. Masáková) We consider exchange of three intervals with permutation $(3,2,1)$. Our aim is to count the cardinality of the set $3\mathrm{iet}(N)$ of factors of length $N$ which belong to the language of an infinite word coding such a transformation. We use the strong relation of 3iet words and 2iet words coding exchange of two intervals, i.e., Sturmian words. The known asymptotic formula $\# 2\mathrm{iet}(N)/N^3\sim\frac1{\pi^2}$ for the number of Sturmian factors allows us to find bounds $\frac1{3\pi^2} + o(1) \leq \# 3\mathrm{iet}(N)/N^4 \leq \frac2{\pi^2} + o(1)$. |
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