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Explicit Ramsey-theoretical functions and applications for graph theory, additive number theory and ordered lists; created in collaboration with Amber Bajaj during an academic mentorship program.

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algorithms applications educational educational-project graph graph-algorithms graph-theory ramsey-theory

ramsey_functions's Introduction

Ramsey functions

About

This project was part of the 2023 University of Toronto Mathematics Mentorship Program and presented at the 2023 Canadian Undergraduate Mathematics Conference.

Developed by

  • Amber Bajaj (mentee)
  • Tonatiuh Matos Wiederhold (mentor)
    Dept. of Mathematics, University of Toronto, Canada.
    [email protected]
This repo contains three things:
  • Custom-made visualization tools appropriate for Ramsey theory. E.g., highlighting monochromatic copies of subgraphs within large networks.
  • Efficient algorithms to compute monochromatic copies of sought subgraphs within large networks. E.g. FindMonochTriangle(H) returns a list of three edges of the same color in constant time.
  • Applications of the above functions to other areas: solving colored linear equations, finding long monotone sublists, etc.

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