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- W4386744642 abstract "A set system ({mathcal F}) is (t)-intersecting, if the size of the intersection of every pair of its elements has size at least (t). A set system ({mathcal F}) is (k)-Sperner, if it does not contain a chain of length (k+1). Our main result is the following: Suppose that (k) and (t) are fixed positive integers, where (n+t) is even and (n) is large enough. If ({mathcal F}subseteq 2^{[n]}) is a (t)-intersecting (k)-Sperner family, then (|{mathcal F}|) has size at most the size of the sum of (k) layers, of sizes ((n+t)/2,ldots, (n+t)/2+k-1). This bound is best possible. The case when (n+t) is odd remains open.Mathematics Subject Classifications: 05D05Keywords: Extremal set theory, Sperner families, intersection theorems" @default.
- W4386744642 created "2023-09-15" @default.
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- W4386744642 date "2023-09-14" @default.
- W4386744642 modified "2023-09-26" @default.
- W4386744642 title "On the sizes of (t)-intersecting (k)-chain-free families" @default.
- W4386744642 doi "https://doi.org/10.5070/c63261991" @default.
- W4386744642 hasPublicationYear "2023" @default.
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