2 research outputs found
More properties of the Fibonacci word on an infinite alphabet
Recently the Fibonacci word on an infinite alphabet was introduced by
[Zhang et al., Electronic J. Combinatorics 24-2 (2017) #P2.52] as a fixed point
of the morphism over
all . In this paper we investigate the occurrence of squares,
palindromes, and Lyndon factors in this infinite word.Comment: 12 pages; minor revision
Some properties of -bonacci words on infinite alphabet
The Fibonacci word on an infinite alphabet was introduced in [Zhang et
al., Electronic J. Combinatorics 2017 24(2), 2-52] as a fixed point of the
morphism , , .
Here, for any integer , we define the infinite -bonacci word
on the infinite alphabet as the fixed point of the morphism on the
alphabet defined for any and any , as
\begin{equation*} \varphi_k(ki+j) = \left\{ \begin{array}{ll} (ki)(ki+j+1) &
\text{if } j = 0,\cdots ,k-2,\\ (ki+j+1)& \text{otherwise}. \end{array} \right.
\end{equation*} We consider the sequence of finite words , where is the prefix of whose length is the
-th -bonacci number. We then provide a recursive formula for the
number of palindromes occur in different positions of . Finally, we
obtain the structure of all palindromes occurring in and based on
this, we compute the palindrome complexity of , for any