English

Simple Algebraic Proofs of Uniqueness for Erd\H{o}s-Ko-Rado Theorems

Combinatorics 2022-01-11 v1 Discrete Mathematics

Abstract

We give simpler algebraic proofs of uniqueness for several Erd\H{o}s-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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Cite

@article{arxiv.2201.02887,
  title  = {Simple Algebraic Proofs of Uniqueness for Erd\H{o}s-Ko-Rado Theorems},
  author = {Yuval Filmus and Nathan Lindzey},
  journal= {arXiv preprint arXiv:2201.02887},
  year   = {2022}
}

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20 pages