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 -uniform hypergraph with hyperedges. We show that this is true when . 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