English

Lagrangians of Hypergraphs II: When colex is best

Combinatorics 2020-03-20 v2

Abstract

A well-known conjecture of Frankl and F\"{u}redi from 1989 states that an initial segment of colex of has the largest Lagrangian of any rr-uniform hypergraph with mm hyperedges. We show that this is true when r=3r=3. We also give a new proof of a related conjecture of Nikiforov and a counterexample to an old conjecture of Ahlswede and Katona.

Keywords

Cite

@article{arxiv.1907.09797,
  title  = {Lagrangians of Hypergraphs II: When colex is best},
  author = {Vytautas Gruslys and Shoham Letzter and Natasha Morrison},
  journal= {arXiv preprint arXiv:1907.09797},
  year   = {2020}
}

Comments

We split our original paper (arXiv:1807.00793v2) into two parts. The first part can be found in arXiv:1807.00793. This is the second part, which consists of 18 pages, including a two-page appendix