2018/07/02 by Gruslys, Vytautas, Letzter, Shoham, Morrison, Natasha
#05C35 #05C65 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1807.00793
An old and well-known conjecture of Frankl and Füredi states that the Lagrangian of an r-uniform hypergraph with m edges is maximised by an initial segment of colex. In this paper we disprove this conjecture by finding an infinite family of counterexamples for all r ≥ 4. We also show that, for sufficiently large t ∈ ℕ, the conjecture is true in the range \binomtr ≤ m ≤ \binomt+1r - \binomt-1r-2.