A General Framework for Studying Finite Rainbow Configurations

Authors

Mike Desgrottes, MSU Undergraduate
Steven Senger, Missouri State UniversityFollow
David Soukup, MSU Undergraduate
Renjun Zhu, MSU Undergraduate

Abstract

Given a coloring of a set, classical Ramsey theory looks for various configurations within a color class. Rainbow configurations, also called anti-Ramsey configurations, are configurations that occur across distinct color classes. We present some very general results about the types of colorings that will guarantee various types of rainbow configurations in finite settings, as well as several illustrative corollaries. The main goal of this note is to present a flexible framework for decomposing finite sets while guaranteeing the existence of some desired structure across the decomposition.

Department(s)

Mathematics

Document Type

Conference Proceeding

DOI

https://doi.org/10.1007/978-3-030-31106-3_5

Publication Date

1-1-2020

Recommended Citation

Desgrottes, Mike, Steven Senger, David Soukup, and Renjun Zhu. "A General Framework for Studying Finite Rainbow Configurations." In Combinatorial and Additive Number Theory, New York Number Theory Seminar, pp. 55-63. Springer, Cham, 2018.

Journal Title

Springer Proceedings in Mathematics and Statistics