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- Title
A GENERAL 2-PART ERDőS-KO-RADO THEOREM.
- Authors
Katona, Gyula O. H.
- 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 ki, ℓi (1 ⩽ i ⩽ m) are given. We prove that if ℱ is an intersecting family containing members F such that |F ℱX1| = ki, |F ∩X2| = ℓi holds for one of the values i (1 ⩽ i ⩽ m) then |ℱ| cannot exceedthe size of the largest subfamily containing one element.
- Subjects
SET theory; MATHEMATICS theorems; CYCLIC permutations; GEOMETRIC vertices; INTEGERS; MATHEMATICAL inequalities
- Publication
Opuscula Mathematica, 2017, Vol 37, Issue 4, p577
- ISSN
1232-9274
- Publication type
Article
- DOI
10.7494/OpMath.2017.37.4.577