Abstract
LetX be ann-element set andℱ be a family of its subsets. Consider the familyℱ x = {F − {x} : F ∈ ℱ} for a givenx ∈ X. We write(m, n) → (m − k, n − 1), when for allℱ with |ℱ| ≥m, there exists an elementx ofX such that|ℱ x| ≥ m − k. We show that (m, n) → (m − 10,n − 1) for allm ≥ 5n and (m, n) → (m − 13,n − 1) for allm ≥ ⌈29n/5⌉.
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Watanabe, M. Some best possible bounds concerning the traces of finite sets II. Graphs and Combinatorics 11, 293–303 (1995). https://doi.org/10.1007/BF01793017
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DOI: https://doi.org/10.1007/BF01793017