Leírás
The next lecture in the Extremal seminar will be on March 12 at 12:30 in the Nagyterem of the Rényi Institute.
Abstract: Let $F$ be a $k\times \l$ (0,1)-matrix. A matrix is {\it simple} if it is a (0,1)-matrix with no repeated columns. A (0,1)-matrix $A$ to said to have a $F$ as a \emph{configuration} if there is a submatrix of $A$ which is a row and column permutation of $F$. In the language of sets, a configuration is a \emph{trace}.
Let $\text{Avoid}(m,F)$ be all simple $m$-rowed matrices $A$ with no configuration $F$. Define $\text{forb}(m,F)$ as the maximum number of columns of any matrix in $\text{Avoid}(m,F)$. The $2\times (p+1)$ (0,1)-matrix $F(0,p,1,0)$ consists of a row of $p$ 1's and a row of one 1 in the remaining column. We determine $\text{forb}(m,F(0,p,1,0))$ for $1\le p\le 9$ and the extremal matrices are characterized. A possibly general extremal construction is given.
Meeting ID: 895 2960 8626
Passcode627606
Invite Link: https://us06web.zoom.us/j/89529608626?pwd=Y4YMgg9b3QvdPmbym7JPMTvyNMpPwb.1