Steiner Triple System Research Project

Set up for a research project involing Steiner Triple Systems. Research in collaboration with Dr. Schroeder through Dakota State University.

Description

This project implements algorithms for generating and analyzing Steiner Triple Systems, including the hill-climbing method using Stinson's Algorithm laid out in Combinatorial Algorithms: Generation, Enumeration, and Design.

Usage

• Using the main.py file, you can generate any number of any order of Steiner Triple Systems
• Using the processSystem method in the graph.py file, you can find the maximum simple cycle length (called the circumference) of a given system
• Using the externalwriting method in the ExternalWriting module, you can continuously generate systems and record information about the current system in output files

Project Structure

• Contains a Scripts folder which houses all the code
  • Process folder contains all scripts that were helpful in the process of creating the current systems, but are currently unused
  • main.py handles simple generation of a given number of a given order of Steiner Triple Systems
  • STSGenerator.py handles the actual generation of the systems
  • graph.py is the graph module (using networkx) that handles the analysis of a given system (finding circumference of system)
  • Multiprocessing_bits.py was designed to analyze the $6233617$ systems with perscribed groups of automorphisms from this paper by Petteri Kaski
  • STS21_vectorization.py is a script that takes in a text file containing STS21s and analyzes their cycles and outputs their "cycle vectors" (defined more clearly in the script's documentation)
  • ExternalWriting.py contains all the methods used for writing mass numbers of generated STS of a given order to a CSV format.
  • PaschChecker.py is a script designed to analyze a file full of STS and tally up which systems are Anti-Pasch and vice-versa
• Contains a Results folder which houses an example output file that the ExternalWriting.py script would generate and a folder called Presentation containing all pertinent materials to a presentation I gave about Steiner Triple Systems and my work on this project.
• Contains a Documentation folder which houses all documentation (information about methodologies and algorithms used in this project)

Acknowledgments

• Dr. Justin Schroeder at Dakota State University as my mentor for this project
• Petteri Kaski from Aalto University for generous sharing of information from his publications