A Generalization of the Bollobás Set Pairs Inequality
| Autor: | Jacques Verstraëte, Jason O'Neill |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Commutative Algebra
Inequality Generalization Applied Mathematics media_common.quotation_subject Mathematics::General Topology Theoretical Computer Science Combinatorics Set (abstract data type) Computational Theory and Mathematics Discrete Mathematics and Combinatorics Geometry and Topology media_common Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 28 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/9627 |
| Popis: | The Bollobás set pairs inequality is a fundamental result in extremal set theory with many applications. In this paper, for $n \geqslant k \geqslant t \geqslant 2$, we consider a collection of $k$ families $\mathcal{A}_i: 1 \leq i \leqslant k$ where $\mathcal{A}_i = \{ A_{i,j} \subset [n] : j \in [n] \}$ so that $A_{1, i_1} \cap \cdots \cap A_{k,i_k} \neq \varnothing$ if and only if there are at least $t$ distinct indices $i_1,i_2,\dots,i_k$. Via a natural connection to a hypergraph covering problem, we give bounds on the maximum size $\beta_{k,t}(n)$ of the families with ground set $[n]$. |
| Databáze: | OpenAIRE |
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