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arXiv · 2206.03323

Fully reducible simple Venn diagrams

Mohammad Farrokhi Derakhshandeh Ghouchan
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Abstract

We generalize Venn diagrams in spaces of arbitrary dimension $\geq 2$ and study simple Venn diagrams with the reducing property. Three equivalent conditions for a simple Venn diagram to reduce it completely and a classification of those diagrams is discussed. For example, we show that a simple $m$-dimensional $n$-Venn diagram is fully reducible if $n\leq m+1$ and conjecture that the converse is also true. An application of the generalized Venn diagrams and some more open problems are given.

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Mohammad Farrokhi Derakhshandeh Ghouchan. 2022-06-05. Fully reducible simple Venn diagrams. https://arxiv.org/abs/2206.03323

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