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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2604.27334 |
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| _version_ | 1866915970447048704 |
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| author | Fang, Yu Feng, Tao Wang, Xiaomiao |
| author_facet | Fang, Yu Feng, Tao Wang, Xiaomiao |
| contents | 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 $S_2(a,b)=\binom{a+b+1}{a+1}-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27334 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The maximum size of the partial ground set of skew Bollobás systems Fang, Yu Feng, Tao Wang, Xiaomiao Combinatorics 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 $S_2(a,b)=\binom{a+b+1}{a+1}-1$. |
| title | The maximum size of the partial ground set of skew Bollobás systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.27334 |