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

The Kolakoski sequence $S$ is the unique element of $\left\lbrace 1,2\right\rbrace^{\omega}$ starting with 1 and coinciding with its own run lengthencoding. We use the parity of the lengths of particular subclasses of initialwords of $S$ as a unifying tool to address the links between the main openquestions - recurrence, mirror/reversal invariance and asymptotic density ofdigits. In particular we prove that recurrence implies reversal invariance, andgive sufficient conditions which would imply that the density of 1s is$\frac{1}{2}$.

Kolakoski Sequence: Links between Recurrence, Symmetry and Limit Density