The Non-Cancelling Intersections Conjecture
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Amarilli, Antoine Monet, Mikaël Suciu, Dan |
| author_facet | Amarilli, Antoine Monet, Mikaël Suciu, Dan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Non-Cancelling Intersections Conjecture Amarilli, Antoine Monet, Mikaël Suciu, Dan Combinatorics Discrete Mathematics 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. |
| title | The Non-Cancelling Intersections Conjecture |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2401.16210 |