15 problems

Let $p$ be prime and define … Here $a$ is understood modulo $p$, $k\in\mathbb{Z}_p^\times$, and $M$ is in the range used for incomplete sums in the paper. Uniform power-sum conject…

Let $p$ be prime, let $\psi_k$ be the arithmetic permutation considered in the paper, and let $D(\psi_k)$ denote its discrepancy. Strong logarithmic discrepancy conjecture. … This…

Let $p$) be prime, let $\mathbb{Z}_p^\times$ denote the nonzero residue classes modulo $p$, and let $\psi_k$ be the arithmetic permutation defined in the surrounding discussion. Wr…

Minimum size conjecture for permutations. Every quasirandom-forcing set of permutations has cardinality at least six.

Minimum size conjecture for 4-point permutations. Every quasirandom-forcing set of $4$-point permutations has cardinality at least eight.

Kohayakawa–Nagle–Rödl–Schacht forcing conjecture. If $H$ is not a forest, then $H$ is KNRS-forcing.

A linear combination of permutation patterns is quasirandom-forcing if it has the quasirandomness-forcing property studied in the paper. The number of terms means the number of per…

Let $\rho^*$ be the quasirandom-forcing linear combination of six permutations … A linear combination is quasirandom-forcing if it has the quasirandomness-forcing property studied…

Let $B$ be an oriented graph, let $\overline{B}$ be its underlying undirected graph obtained by forgetting edge directions, and call $B$ directed-forcing when it has the directed f…

Let $f\colon \mathbb{Z}/2^n\mathbb{Z}\to\{\pm1\}$ be a Boolean function. Say that $f$ has $(\delta,k)$-$\mathbb{R}$-regularity and that it has $\epsilon$-$\mathbb{Z}/2^n\mathbb{Z}$…

Higher-wise independence conjecture. For any prime power $q$ and integers $4\leq\ell<t$, all but $o(n^\ell)$ sets of $\ell$ vertices in $\operatorname{NG}(q,t)$ have…

Let $H$ be a graph, let $p\in[0,1]$, and let $G$ be a graph. The property $\mathcal{P}_{H,p}^{*}(\delta)$ means that every $U\subseteq V(G)$ satisfies … Let…

Let $H$ be a fixed bipartite graph of girth $g$, and let $p$ be a fixed constant with $0<p<1$. For each $\epsilon>0$, there is a parameter $\delta=\Omega(\epsilon^g)$ such that any…

Linial–Luria's conjecture. There exist arbitrarily large Latin squares $L$ such that, for every box $T=I\times X\times Q$,

A graph is called forcing if it is $p$-forcing for every $0<p<1$, where a graph $H$ is $p$-forcing when, for every graph sequence of edge density tending to $p$, the condition…