## Welcome to my mathematical world!

On this website I present some of my work, thoughts and ideas on selected topics in mathematics. These range from conjectures over abstract ideas to rigorous proofs. All my work is common that I always try to create something new, to think in a new direction. My main fields of research are number theory, combinatorics and graph theory. If a problem has grabbed me, I worked on it over many years. Some texts on this site are just available in German. If you have any questions, please send me an email.

In the hope to enrich the mathematical world a little bit, enjoy reading and exploring.

## Mike Winkler

**NEW**: On the existence of 4-regular matchstick graphs (arXiv 1705.00293)

**NEW**: The Recursive Stopping Time Structure of the 3x + 1 Function (arXiv 1709.03385), under review (latest update)

**NEW **: First 4-regular matchstick graph which consists only of vertex-to-vertex unit triangles without additional triangles. These graph consists of 63072 triangles and has a rotational symmetry of order 292. (Pic1 Pic2 Pic3 Pic4)

The currently smallest example contains 9200 triangles and has a rotational symmetry of order 100. (Pic1 Pic2)

Note: The latest updates of my arXiv preprints can be found first on my homepage.

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since 30.04.2015.

Last update on October 11, 2018.