Abstract:In 1939, Richard Rado showed that any complex matrix is partition regular over ރ if and only if it satisfies the columns condition. Recently, Hogben and McLeod explored the linear algebraic properties of matrices satisfying partition regularity. We further the discourse by generalizing the notion of partition regularity beyond systems of linear equations to topological surfaces and graphs. We begin by defining, for an arbitrary matrix , the metric space (M , δ). Here, M is the set of all matrices equivalent … Show more
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