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Lagrangians of hypergraphs II: When colex is best
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2021-04-23 , DOI: 10.1007/s11856-021-2132-2
Vytautas Gruslys , Shoham Letzter , Natasha Morrison

A well-known conjecture of Frankl and Füredi from 1989 states that an initial segment of the colexicographic order has the largest Lagrangian of any r-uniform hypergraph with m hyperedges. We show that this is true when r = 3. We also give a new proof of a related conjecture of Nikiforov for large t and a counterexample to an old conjecture of Ahlswede and Katona.



中文翻译:

超图的拉格朗日II:当colex最好时

1989年的弗兰克(Frankl)和弗雷迪(Füredi)的一个著名猜想指出,在所有具有m个超边缘的r一致超图中,共阴学秩序的初始部分具有最大的拉格朗日数。我们证明当r = 3时,这是正确的。我们还给出了有关Nikiforov对于大t的猜想的新证明,以及对Ahlswede和Katona的旧猜想的反例。

更新日期:2021-04-24
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