English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For any integer $k>2$, the infinite $k$-bonacci word $W^{(k)}$, on theinfinite alphabet is defined as the fixed point of the morphism$\varphi_k:\mathbb{N}\rightarrow \mathbb{N}^2 \cup \mathbb{N}$, where\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{if } j =k-1. \end{array} \right.\end{equation*} The finite $k$-bonacci word $W^{(k)}_n$ is then defined as theprefix of $W^{(k)}$ whose length is the $(n+k)$-th $k$-bonacci number. Weobtain the structure of all square factors occurring in $W^{(k)}$. Moreover, weprove that the critical exponent of $W^{(k)}$ is $3-\frac{3}{2^k-1}$. Finally,we provide all critical factors of $W^{(k)}$.

On square factors and critical factors of $k$-bonacci words on infinite alphabet