Uniqueness for 2-Intersecting Families of Permutations and Perfect Matchings

TL;DR

This paper characterizes the largest 2-intersecting families of permutations and perfect matchings, providing a comprehensive understanding of their structure for all sizes.

Contribution

It offers a complete characterization of the maximum 2-intersecting families of permutations and perfect matchings for any size n.

Findings

Identifies the structure of largest 2-intersecting families

Provides characterization valid for all n ≥ 2

Advances understanding of intersecting combinatorial families

Abstract

We give a characterization of the largest $2$-intersecting families of permutations of $\{1,2,\ldots,n\}$ and of perfect matchings of the complete graph $K_{2n}$ for all $n \geq 2$.