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On the dimension of the cartesian product of relations and orders

Authors:	Klaus Reuter

Institution:	(1) FB Mathematik, Technische Hochschule Darmstadt, 6100 Darmstadt, West Germany

Abstract:	It is known that for incidence structures $\mathbb{K}$ and $\mathbb{L}$ , max $\{ f{\text{ dim }}\mathbb{K}{\text{, }}f{\text{ dim }}\mathbb{L}{\text{\} }} \leqslant {\text{ }}f{\text{ dim }}\mathbb{K}{\text{ }}x{\text{ }}\mathbb{L} \leqslant f{\text{ dim }}\mathbb{K}{\text{ + }}f{\text{ dim }}\mathbb{L}$ , wheref dim stands for Ferrers relation. We shall show that under additional assumptions on $\mathbb{K}$ and $\mathbb{L}$ , both bounds can be improved. Especially it will be shown that the square of a three-dimensional ordered set is at least four-dimensional.

Keywords:	06A10
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