-
Rényi, Kutyás terem + Zoom
-
-
-
-
-
-

Description

Abstract:
Write $K^{(k)}_{n}$ for the complete $k$-graph on $n$ vertices. For $2 \leq k \leq g < r$ integers, let $\pi\left(n, K^{(k)}_{g}, K^{(k)}_r\right)$ be the maximum density of $K^{(k)}_{g}$ in $n$ vertex $K^{(k)}_{r}$-free $k$-graphs. The main contribution is the upper bound: $\pi\left(n, K^{(k)}_{g}, K^{(k)}_r\right) \leq \left(1 + O\left(n^{-1}\right) \right)\prod_{m=k}^{g} \left(1 - \frac{{m-1}\choose{k-1}}{{r-1}\choose{k-1}} \right).$ The proof uses techniques from the theory of flag algebras to derive linear relations between different densities. Additionally a simple flag algebraic certificate will be given for $\lim_{n \rightarrow \infty} \pi \left(n, K^{(3)}_4, K^{(3)}_5 \right) = 3/8$.

 

The lecture can be followed by zoom: