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- W4291208051 abstract "For a family $mathcal F$, let $mathcal D(mathcal F)$ stand for the family of all sets that can be expressed as $Fsetminus G$, where $F,Gin mathcal F$. A family $mathcal F$ is intersecting if any two sets from the family have non-empty intersection. In this paper, we study the following question: what is the maximum of $|mathcal D(mathcal F)|$ for an intersecting family of $k$-element sets? Frankl conjectured that the maximum is attained when $mathcal F$ is the family of all sets containing a fixed element. We show that this holds if $n ge 50kln k$ and $k ge 50$. At the same time, we provide a counterexample for $n< 4k$." @default.
- W4291208051 created "2022-08-13" @default.
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- W4291208051 date "2021-06-09" @default.
- W4291208051 modified "2023-09-29" @default.
- W4291208051 title "Best possible bounds on the number of distinct differences in intersecting families" @default.
- W4291208051 doi "https://doi.org/10.48550/arxiv.2106.05355" @default.
- W4291208051 hasPublicationYear "2021" @default.
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