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The Non-Cancelling Intersections Conjecture

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arxiv 2401.16210 v1 pith:UFNB2WI3 submitted 2024-01-29 math.CO cs.DM

Antoine Amarilli , Mikaël Monet , Dan Suciu This is my paper · ORCID
classification math.COcs.DM
keywords conjectureintersectionsunionexpressmeasuretermsbooleancomplement
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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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Cited by 1 Pith paper

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  1. On the Complexity of Language Membership for Probabilistic Words

    cs.FL 2025-10 conditional novelty 7.0 of 10

    Probabilistic membership for context-free languages is in PTIME for unambiguous and poly-slicewise-unambiguous languages, #P-hard for some unions of two linear unambiguous CFLs, and tractable via complement-capable ci...

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