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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2604.27334 |
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Sommario:
- A skew Bollobás system $\mathcal{P}=\{(A_i,B_i):1\leq i\leq m\}$ is a collection of pairs of disjoint subsets of $[n]$ such that $A_i\cap B_j\ne\emptyset$ for any $1\leq i<j\leq m$. Denote by $S_1(a, b)$ or $S_2(a, b)$ the maximum size of $\bigcup_{i=1}^m A_i$ or $\bigcup_{i=1}^m B_i$, respectively, over all possible skew Bollobás systems $\mathcal{P}=\{(A_i,B_i):1\leq i\leq m\}$ satisfying $|A_i| \leq a$ and $|B_i| \leq b$ for all $i \in [m]$. It is shown that for any non-negative integers $a$ and $b$, $S_1(a,b)=\binom{a+b+1}{a}-1$ and $S_2(a,b)=\binom{a+b+1}{a+1}-1$.