Drawing the Kontsevich Graphs in LaTeX

Kerkhove, Sylvia (2020) Drawing the Kontsevich Graphs in LaTeX. Bachelor's Thesis, Mathematics.

Preview	Text bMATH_2020_KerkhoveSS.pdf Download (963kB) | Preview
	Text toestemming.pdf Restricted to Registered users only Download (95kB)

Abstract

Kontsevich graphs are a class of oriented graphs on two sinks,build of wedges. Such graphs are naturally encoded by a list of pairs of target vertices of each wedge. This project is about semi-automatic drawing of Kontsevich graphs in the LaTeX picture environment, that is, finding the Cartesian coordinates of the top vertex of each wedge such that the result can be drawn in the picture environment while satisfying several requirements. An algorithm to achieve this was proposed by A.V.Kiselev. This algorithm first calculates the aforementioned coordinates based on randomly assigned inclines of the edges. It then filters out the bad drawings and finally uses a penalty function to determine the most beautiful drawing. The goal of this project is to tune and modify this penalty function so that its output guarantees aesthetically pleasing drawings. I have implemented this algorithm in SageMath (with the help of R. Buring). In this paper I contribute several modifications to the existing algorithm and I analyse which part of the penalty function is most important to draw nice graphs. This whole project is presently applied to drawing – for the first time! – a significant number of the 247 four-wedge graphs which have been discovered by Buring and Kiselev in [arXiv:1702.00681] at the fourth order of the parameter in the expansion of noncommutative associative star-product by Kontsevich.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Kiselev, A.V.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	14 Jul 2020 10:54
Last Modified:	14 Jul 2020 10:54
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/22654

Actions (login required)

View Item