Leírás
Abstract:
We will present the paper of Das, Gan and Sudakov (arXiv:1305.6715v1). The famous theorem of
Erdos-Ko-Rado from 1961 states that a set system of pairwise intersecting $k$-elements subsets of [n] has
size at most ${n-1}\choose{k-1}$. In 1980 Ahlswede asked how many disjoint pairs must appear in any set system
of size which exceeds this threshold. Katona and Ahslwede gave the answer for $k=2$, and in 2003 Bollobas and
Leader conjectured that one of the systems $A_{r,l} = \{ A \in {{[n]}\choose{k}}: |A \cap [r]| \geq l \}$ minimizes the
number of disjoint pairs for every $k$. During my talk we will follow the results of Das, Gan and Sudakov, who
verified this conjecture for small systems, showing that initial segments of the lexicographical ordering minimize
the number of disjoint pairs.
The lecture can be followed by zoom:
- Zoom link: https://us06web.zoom.us/j/81239725712?pwd=eDlXNXR1cUhVbWRNbUdEc1dEcWo2dz09
- Meeting ID: 812 3972 5712
- Passcode: 670457