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Triangular Ramsey Numbers

The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about triangular sets are proved. This game is easy enough that young children are able to play. The most basic variations of this game are analyzed and theorems about winning strategies and the existence of draws are proved. The game of Mines is then used to define triangular Ramsey numbers. Lower bounds are found for these triangular Ramsey numbers using the probabilistic method and the theorems about triangular sets.

preprint2016arXivOpen access
Timothy TrujilloConnor MattesZachary ChaneyJed Menard
math.CO
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Open access4 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Timothy TrujilloConnor MattesZachary ChaneyJed Menard

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