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- W3025808515 abstract "A fundamental result in extremal set theory is Katona's shadow intersection theorem, which extends the Kruskal-Katona theorem by giving a lower bound on the size of the shadow of an intersecting family of $k$-sets in terms of its size. We improve this classical result and a related result of Ahlswede, Aydinian, and Khachatrian by proving tight bounds for families that can be quite small. For example, when $k=3$ our result is sharp for all families with $n$ points and at least $3n-7$ triples. Katona's theorem was extended by Frankl to families with matching number $s$. We improve Frankl's result by giving tight bounds for large $n$." @default.
- W3025808515 created "2020-05-21" @default.
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- W3025808515 date "2020-05-14" @default.
- W3025808515 modified "2023-09-25" @default.
- W3025808515 title "Tight bounds for Katona's shadow intersection theorem" @default.
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- W3025808515 doi "https://doi.org/10.48550/arxiv.2005.06999" @default.
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