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.
翻译:我们给出了更简单的代数证明,以证明Erd\H{o}s-Ko-Rado(Erd\H{o}s-Ko-Rado)的一些结果的独特性,即,罐形交叉式家庭是唯一最大的交叉式家庭。 使用这些技术,我们将最大的两部分交叉式家庭定性为完美超配型家庭,解决了米格尔、希拉齐和史蒂文斯最近的猜想。