Combinatorics: Amir Yehudayoff (Technion) TBA

Date: 
Location: 
Rothberg B221 (CS building)
Speaker: Misha Tyomkyn (TAU)
Title: Lagrangians of hypergraphs and the Frankl-Furedi conjecture
Abstract:
Frankl and Furedi conjectured in 1989 that the maximum Lagrangian of
all r-uniform hypergraphs of given size m is realised by the initial
segment of the colexicographic order. For r=3 this was partially solved
by Talbot, but for r\geq 4 the conjecture was widely open. We verify
the conjecture for all r\geq 4, whenever
$\binom{t-1}{r} \leq m \leq \binom{t}{r}- \gamma_r t^{r-2}$
for a constant $\gamma_r>0$. This range includes the principal case
$m=\binom{t}{r}$ for large enough $t$.