Attila Sali: Multi-valued forbidden numbers of two-rowed configurations -- the missing cases

The next lecture in the Extremal seminar will be on December 12 at 12:30
in the Nagyterem of the Rényi Institute.

Speaker: Attila Sali

Title: Multi-valued forbidden numbers of two-rowed configurations -- the missing cases

Abstract: The talk considers extremal combinatorics questions in the language of matrices. An $s$-matrix is a matrix with entries in $\{0,1,\ldots, s-1\}$. An $s$-matrix is simple if it has no repeated columns. A matrix $F$ is a configuration in a matrix $A$, denoted $F\prec A$, if it is a row/column permutation of a submatrix of $A$. $\Avoid(m,s,F)$ is the set of $m$-rowed, simple $s$-matrices not containing a configuration of $F$ and $\forb(m,s, F)=\max\{|A|\colon A \in \Avoid(m,s,F)\}$. Dillon and Sali initiated the systematic study of $\forb(m,s, F)$ for $2$-matrices $F$, and computed $\forb(m,s, F)$ for all 2-rowed $F$ when $s>3$. In this paper we tackle the remaining cases when $s=3$. In particular, we determine the asymptotics of $\forb(m,3,p\cdot K_2)-\forb(m,3,p\cdot I_2)$ for $p>3$, where $K_2$ is the $2\times 4$ simple $2$-matrix and $I_2$ is the $2\times 2$ identity.

ZOOM

Meeting ID 825 2991 8779

Passcode 791691

https://us06web.zoom.us/j/82529918779?pwd=WtyNBEuyAuq4Lq2akfHHSY0aOR9VVm.1