Author:
Hwang Kyung-Won,Kim Younjin,Sheikh Naeem N.
Abstract
A family F is an intersecting family if any two members have a nonempty intersection. Erdős, Ko, and Rado showed that | F | ≤ n − 1 k − 1 holds for a k-uniform intersecting family F of subsets of [ n ] . The Erdős-Ko-Rado theorem for non-uniform intersecting families of subsets of [ n ] of size at most k can be easily proved by applying the above result to each uniform subfamily of a given family. It establishes that | F | ≤ n − 1 k − 1 + n − 1 k − 2 + ⋯ + n − 1 0 holds for non-uniform intersecting families of subsets of [ n ] of size at most k. In this paper, we prove that the same upper bound of the Erdős-Ko-Rado Theorem for k-uniform intersecting families of subsets of [ n ] holds also in the non-uniform family of subsets of [ n ] of size at least k and at most n − k with one more additional intersection condition. Our proof is based on the method of linearly independent polynomials.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Cited by
1 articles.
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