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Mathematics Combinatorics Intersection (aeronautics) Generalization Set (abstract data type) Discrete mathematics Computer science Mathematical analysis Engineering Programming language Aerospace engineering

Balázs Patkós , Źsolt Tuza , Máté Vizer ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1016/j.disc.2023.113506 · OA: W4380997473

We introduce the following generalization of set intersection via characteristic vectors: for n,q,s,t≥1 a family F⊆{0,1,…,q}n of vectors is said to be s-sum t-intersecting if for any distinct x,y∈F there exist at least t coordinates, where the entries of x and y sum up to at least s, i.e. |{i:xi+yi≥s}|≥t. The original set intersection corresponds to the case q=1,s=2. We address analogs of several variants of classical results in this setting: the Erdős–Ko–Rado theorem and the theorem of Bollobás on intersecting set pairs.