Elementary Techniques for Erdos-Ko-Rado-like Theorems

TL;DR

This paper introduces elementary methods to generalize the Erdos-Ko-Rado Theorem across various combinatorial objects and extends results to systems with Hamming intersection.

Contribution

It provides new elementary techniques for deriving Erdos-Ko-Rado-like theorems and extends these results to Hamming intersection systems.

Findings

Generalized Erdos-Ko-Rado theorems for multiple combinatorial classes

Extended results to Hamming intersection systems

Provided elementary proof methods

Abstract

The well-known Erdos-Ko-Rado Theorem states that if F is a family of k-element subsets of {1,2,...,n} (n>2k-1) such that every pair of elements in F has a nonempty intersection, then |F| is at most $\binom{n-1}{k-1}$. The theorem also provides necessary and sufficient conditions for attaining the maximum. We present elementary methods for deriving generalizations of the Erdos-Ko-Rado Theorem on several classes of combinatorial objects. We also extend our results to systems under Hamming intersection.