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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The Farey sequence $\mathcal{F}(Q)$ at level $Q$ is the sequence ofirreducible fractions in $[0, 1]$ with denominators not exceeding $Q$, arrangedin increasing order of magnitude. A simple ``next-term'' algorithm exists forgenerating the elements of $\mathcal{F}(Q)$ in increasing or decreasing order.That algorithm, along with a number of other properties of the Farey sequence,was encoded by F. Boca, C. Cobeli, and A. Zaharescu into what is now known asthe Boca-Cobeli-Zaharescu (BCZ) map, and used to attack several problems thatcan be described using the statistics of subsets of the Farey sequence. In thispaper, we derive the Boca-Cobeli-Zaharescu map analogue for the discrete orbits$\Lambda_q = G_q(1, 0)^T$ of the linear action of the Hecke triangle groups$G_q$ on the plane $\mathbb{R}^2$ starting with a Stern-Brocot tree analoguefor the said orbits. We derive the next-term algorithm for generating theelements of $\Lambda_q$ in vertical strips in increasing order of slope, andpresent a number of applications to the statistics of $\Lambda_q$.

The Boca-Cobeli-Zaharescu Map Analogue for the Hecke Triangle Groups $G_q$