Ramsey properties of products of chains

Published 11 Dec 2020 in math.CO | (2012.06507v4)

Abstract: Let $\mathbf{k}$ denote the totally ordered set (or chain) on $k$ elements. The product $\mathbf{k}^{t=\mathbf{k}\times\cdots\times\mathbf{k}$} is a poset called a grid. This paper discusses several loosely related results on the Ramsey theory of grids. Most of the results involve some application of the Product Ramsey Theorem.

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