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arXiv · 2401.16210

The Non-Cancelling Intersections Conjecture

Antoine Amarilli·Mikaël Monet·Dan Suciu
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Abstract

In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a union of sets in terms of the measure of some of their intersections using the inclusion-exclusion formula, then we can express the union as a set from these same intersections via the set operations of disjoint union and subset complement. We also present a partial result towards establishing the conjecture.

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Antoine Amarilli, Mikaël Monet, Dan Suciu. 2024-01-29. The Non-Cancelling Intersections Conjecture. https://arxiv.org/abs/2401.16210

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