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- W2963826084 abstract "In this short note, we address two problems in extremal set theory regarding intersecting families. The first problem is a question posed by Kupavskii: is it true that given two disjoint cross-intersecting families A , B ⊂ [ n ] k , they must satisfy min { | A | , | B | } ≤ 1 2 n − 1 k − 1 ? We give an affirmative answer for n ≥ 2 k 2 , and construct families showing that this range is essentially the best one could hope for, up to a constant factor. The second problem is a conjecture of Frankl. It states that for n ≥ 3 k , the maximum diversity of an intersecting family F ⊂ [ n ] k is equal to n − 3 k − 2 . We are able to find a construction beating the conjectured bound for n slightly larger than 3 k , which also disproves a conjecture of Kupavskii." @default.
- W2963826084 created "2019-07-30" @default.
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- W2963826084 date "2019-02-01" @default.
- W2963826084 modified "2023-09-29" @default.
- W2963826084 title "Two extremal problems on intersecting families" @default.
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- W2963826084 doi "https://doi.org/10.1016/j.ejc.2018.08.009" @default.
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