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

In this article, the goal is to find the shortest presentation of a matrix $A\in PSL(2,\mathbb{Z})$ in terms of the so-called continuant matrices which aremost known for their role in continued fraction theory. In chapter 7 ofarXiv:1811.01229, Morier-G\'enoud and Ovsienko investigate this problem withthe restriction that all coefficients of the continuant matrices are positive.Now, the goal is to determine the shortest presentation allowing all integercoefficients. To determine this minimal presentation, a few characteristictransformations will be introduced. It will also be investigated under whichconditions such a minimal presentation becomes unique. The results are alsogeneralized on conjugacy classes in $PSL(2,\mathbb{Z})$.  If you wish to contact the author or you have some questions related to thiswork, feel free to write an email to christian.streib@online.de.

Minimal Presentation of $PSL(2,\mathbb{Z})$ Using Continuant Matrices with Integer Coefficients