A new proof of the Erdös-Ko-Rado theorem for intersecting families of permutations

Erdös-Ko-Rado-Type Theorems for Colored Sets

An Erdős-Ko-Rado-type theorem was established by Bollobás and Leader for q-signed sets and by Ku and Leader for partial permutations. In this paper, we establish an LYM-type inequality for partial permutations, and prove Ku and Leader’s conjecture on maximal k-uniform intersecting families of partial permutations. Similar results on general colored sets are presented.

Erdös-Ko-Rado from intersecting shadows

A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős–Ko–Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corres...

Towards a Katona type proof for the 2-intersecting Erdös-Ko-Rado theorem

Towards a Katona Type Proof for the 2-intersecting Erdos-Ko-Rado Theorem

We study the possibility of the existence of a Katona type proof for the Erdős-Ko-Rado theorem for 2and 3-intersecting families of sets. An Erdős-Ko-Rado type theorem for 2-intersecting integer arithmetic progressions and a model theoretic argument show that such an approach works in the 2-intersecting case.

THE EIGENVALUE METHOD FOR CROSS t-INTERSECTING FAMILIES

We show that the Erdős–Ko–Rado inequality for t-intersecting families of subsets can be easily extended to an inequality for cross t-intersecting families by using the eigenvalue method. The same applies to the case of t-intersecting families of subspaces. The eigenvalue method is one of the proof techniques to get Erdős–Ko–Rado type inequalities for t-intersecting families, for example, a proo...