Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.11997 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- Given a point set $S$ in $\mathbb{R}^d$, a family of sets is $S$-intersecting if its members have a point in common in $S$. Recently, Edwards and Soberón proved a fractional version of Halman's theorem for axis-parallel boxes, showing that every finite family $F$ of axis-parallel boxes in $\mathbb{R}^d$ with positive density of $S$-intersecting $(d+1)$-tuples contains an $S$-intersecting subfamily of size linear in $|F|$. We prove that qualitatively the same conclusion can be achieved if the density of $S$-intersecting pairs is sufficiently large.