Simple Algebraic Proofs of Uniqueness for Erdős-Ko-Rado Theorems

2022/01/08 by Filmus, Yuval, Nathan Lindzey, Lindzey, Nathan
Engineering · Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2201.02887

openalex publication_date 2022/01/08 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We give simpler algebraic proofs of uniqueness for several Erd\Hos-Ko-Rado results, i.e., that the canonically intersecting families are the only largest intersecting families. Using these techniques, we characterize the largest partially 2-intersecting families of perfect hypermatchings, resolving a recent conjecture of Meagher, Shirazi, and Stevens.

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