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Corpus ID: 248496863

Intersections and Distinct Intersections in Cross-intersecting Families

@inproceedings{Frankl2022IntersectionsAD,
title={Intersections and Distinct Intersections in Cross-intersecting Families},
author={Peter Frankl and Jian Wang},
year={2022}
}

Let F , G be two cross-intersecting families of k -subsets of { 1 , 2 , . . ., n } . Let F ∧ G , I ( F , G ) denote the families of all intersections F ∩ G with F ∈ F , G ∈ G , and all distinct intersections F ∩ G with F 6 = G, F ∈ F , G ∈ G , respectively. For a ﬁxed T ⊂ { 1 , 2 , . . ., n } , let S T be the family of all k -subsets of { 1 , 2 , . . ., n } containing T . In the present paper, we show that |F ∧G| is maximized when F = G = S { 1 } for n ≥ 2 k 2 +8 k , while surprisingly |I ( F… Expand

Two families F , G of k -subsets of { 1 , 2 , . . ., n } are called non-trivial cross-intersecting if F ∩ G 6 = ∅ for all F ∈ F , G ∈ G and ∩{ F : F ∈ F} = ∅ = ∩{ G : G ∈ G} . In the present paper,… Expand

We consider k -graphs on n vertices, that is, F ⊂ (cid:0) [ n ] k (cid:1) . The recent advances of Keller and Lifshitz [31] gave a new impetus to extend the validity of previously known intersection… Expand

2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set… Expand