Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 5.10.2010 |
| Speaker: | Ondřej Turek, Laboratory of Physics, Kochi University of Technology, Japan |
| Title: | Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words |
| Abstract: | A word $u$ defined over an alphabet $A$ is $c$-balanced ($c\in\mathbb{N}$) if for all pairs of factors $v,w$ of $u$ of the same length and for all letters $a\in A$, the difference between the number of letters $a$ in $v$ and $w$ is less than or equal to $c$. In this paper we consider a ternary alphabet $A =\{L, S,M\}$ and a class of substitutions $\varphi_p$ defined by $\varphi_p(L) = L^pS$, $\varphi_p(S) = M$, $\varphi_p(M) = L^{p-1}S$ where $p > 1$. We prove that the fixed point of $\varphi_p$ is 3-balanced and that its Abelian complexity is bounded from above by the value 7, regardless of the value of $p$. We also show that both these bounds are optimal, i.e., they cannot be improved. |
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