A general 2-part Erd\H os-Ko-Rado theorem

2017/03/01 by Gyula O. H. Katona, Katona, Gyula O. H.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1703.00287

openalex publication_date 2017/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A two-part extension of the famous Erdős-Ko-Rado Theorem is proved. The underlying set is partitioned into X₁ and X₂. Some positive integers k_i, ℓ_i (1≤ i≤ m) are given. We prove that if \cal F is an intersecting family containing members F such that |F∩ X₁|=k_i, |F∩ X₂|=ℓ_i holds for one of the values i (1≤ i≤ m) then |\cal F| cannot exceed the size of the largest subfamily containing one element.

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