9 problems

Let $t\geq 2$, and let $A$ be a zero-one matrix. The matrix is assumed to contain at most $t$ $1$-entries in each row. Let $\operatorname{ex}(n,A)$ denote its extremal number. Meth…

Korándi–Pach–Tomon's strong conjecture. For every ordered forest bigraph $H$, there exists $\varepsilon>0$ with the following property: if $G$ is an ordered bigraph that does not c…

Korándi–Pach–Tomon's conjecture. Let $H$ be an ordered bigraph such that both $H$ and its bicomplement are forests. Then there exists $\varepsilon>0$ with the following property: i…

Let $I_k$ be the $k\times k$ identity matrix, and let $J_k$ be the permutation pattern obtained from $I_k$ by moving its first row after its last row. For a pattern $P$, let…

Let $P$ be a $0$-$1$ matrix that is the incidence matrix of a bipartite tree, and let $ex(P,n)$ denote the maximum number of $1$-entries in an $n\times n$ $0$-$1$ matrix avoiding…

Let ${\operatorname{forbmax}}(m, r, \mathcal{F})=\max_{m'\leq m}{\operatorname{forb}}(m', r, \mathcal{F})$ denote the maximum of the forbidden-submatrix function up to $m$, where…

Let a simple $m\times n$ $(0,1)$ matrix be a matrix with pairwise distinct columns, and let a contribution mean the configuration defined earlier in the paper. Contribution conject…

Let $F$ be a $k\times l$ $(0,1)$ matrix. Write $\mathrm{fs}(m,F)$ for the maximum number of columns in a simple $m$-rowed $(0,1)$ matrix that contains no induced submatrix equal to…

Let $F$ be a fixed $(0,1)$-matrix. For matrices $M$ and $N$, write $[M\,|\,N]$ for their horizontal concatenation and let $k\cdot M$ denote the concatenation of $k$ copies of $M$.…