15 problems

Let $F$ be a $k\times \ell$ matrix with $F\ne \begin{bmatrix}0\\ 1\end{bmatrix}$. Let $I_k$ be the $k\times k$ identity matrix, $I_k^c$ its (0,1)-complement, and $T_k$ the…

Let $t$ be given, and let ${\mathrm{forb}}(m,F(0,2^{t-2}+1,1,0))$ denote the maximum number of columns in an $m$-rowed binary matrix avoiding the configuration $F(0,2^{t-2}+1,1,0)$…

Anstee–Sali conjecture. The extremal number for $M$ is governed by a product construction using singleton, cosingleton, and chain factors.

Let $F$ be a simple $k\times \ell$ $(0,1)$-matrix. A product of matrices is obtained by stacking, in order, one column from each factor; the factors here are identity matrices $I$,…

General equality conjecture.

Let $H(m,2)$ and $H_2(m,2)$ denote the two quantities defined in the paper for integers $m\geq 3$. Equality conjecture. … Consequently, the paper's forbidden-configuration function…

Let $\mathcal{F}\subseteq\mathcal{P}(n)$ be a family of subsets, and let $F$ be its $n\times|\mathcal{F}|$ incidence matrix. For a binary matrix $M$, write $X(M)$ for the associate…

Anstee–Raggi monotonicity conjecture. For sufficiently large $m$,

The special $d$-dimensional simplex $\mathcal{S}_d$ is a hypergraph consisting of $d+1$ sets $A_1,\ldots,A_{d+1}$ such that … for every $i\in[d+1]$, and the sets…

A minimal cubic configuration is a minimal configuration associated with the cubic forbidden-configuration problem; a configuration is minimal when deleting any row or column destr…

Forbidden Berge hypergraph conjecture for the 4-cycle.

Let ${\mathcal A} \subseteq {\mathcal P}[n]$ be a family of subsets with $|A\setminus B|\neq 1$ for all $A,B\in\mathcal A$. For $r\in\{0,\ldots,n-1\}$, let ${\mathcal A}^{*}$ be th…

Let $F$ be a configuration and let $X(F)$ be the exponent defined by the Anstee–Sali product construction. Anstee's NP-hardness conjecture. Determining $X(F)$ from $F$ is NP-hard.…

Let $\mathcal{F}$ be a possibly infinite set of systems of induced equations, and let a Boolean function be $\mathcal{F}$-free when it contains no induced solution of any system in…

Let $\mathcal{F}=\{(M^1,\boldsymbol{\sigma}^1),(M^2,\boldsymbol{\sigma}^2),\ldots\}$ be a possibly infinite set of induced systems of linear equations. A Boolean function is…