Intersections of iterated shadows
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912026416119808 |
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| author | Chau, Hou Tin Ellis, David Tiba, Marius |
| author_facet | Chau, Hou Tin Ellis, David Tiba, Marius |
| contents | We show that if $\mathcal{A} \subset {[n] \choose n/2}$ with measure bounded away from zero and from one, then the $Ω(\sqrt{n})$-iterated upper shadows of $\mathcal{A}$ and $\mathcal{A}^c$ intersect in a set of positive measure. This confirms (in a strong form) a conjecture of Friedgut. It can be seen as a stability result for the Kruskal--Katona theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_05487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersections of iterated shadows Chau, Hou Tin Ellis, David Tiba, Marius Combinatorics Classical Analysis and ODEs 05D05 We show that if $\mathcal{A} \subset {[n] \choose n/2}$ with measure bounded away from zero and from one, then the $Ω(\sqrt{n})$-iterated upper shadows of $\mathcal{A}$ and $\mathcal{A}^c$ intersect in a set of positive measure. This confirms (in a strong form) a conjecture of Friedgut. It can be seen as a stability result for the Kruskal--Katona theorem. |
| title | Intersections of iterated shadows |
| topic | Combinatorics Classical Analysis and ODEs 05D05 |
| url | https://arxiv.org/abs/2409.05487 |