57 problems

Let $Q(n)$ denote the number of classical $n$-queens configurations, and let $T(n)$ denote the number of toroidal $n$-queens configurations. A classical configuration places $n$ qu…

Bounded-correction conjecture. For every such 4-tuple,

Békessy–Békessy–Komlós conjecture. The relative error of this approximation is $O\left(N^{-1}\right)$ as $N\longrightarrow +\infty$.

Asymptotic conjecture. When $p$ is large with $r$ fixed, or $r$ is large with $p$ fixed, one has

Monotonic growth-constant conjecture. For fixed $m$, the limit $\alpha_m$ exists, and

Let $(\overline{a},f_0,f_1)$ be general choices satisfying … In the asymptotic enumeration of admixed arrays subject to row and column constraints, the independence heuristic is th…

Conway–Guttman conjecture. For $q in {4321,4312}$, there is a constant $K$ such that

For a fixed integer $k\geq 1$, let $P'(2,n,k)$ denote the number of prime 2-ball, $k$-hand passing patterns of length $n$. As $n$ tends to infinity, Exponential lower-bound conject…

Let $\mathcal{C}$ be a permutation class, and let $\mathcal{C}^{\circ}$ be the set of derangements in $\mathcal{C}$. Write $\mathcal{C}_n$ and $\mathcal{C}^{\circ}_n$ for their mem…

Let $C_n$ be the $n$th Catalan number, and let $d_n$ be the number of derangements among the $123$-avoiding permutations of length $n$. The source considers an asymptotic form…

Mayhew–Newman–Welsh conjecture. Almost all geometric lattices are paving lattices, in the precise sense that

Arras–Joos conjecture. As $t$ tends to infinity,

For integers $d,n\geq 2$, let $\Omega_n^d$ be the polytope of $d$-dimensional polystochastic matrices, and let $V(n,d)$ denote its number of vertices. For fixed $d$, write…

Asymptotic enumeration conjecture. For every $m\geq 1$, the number of reduced $((2m+1))$-historic trees with $n$ vertices is asymptotically equal to

Let $AD(n)$ be the Aztec diamond of order $n$. Let $O(2n,[2n])$ be the set of off-diagonally symmetric domino tilings of $AD(2n)$ with no boundary defect, and let $D(2n-1)$ be the…

Let $\operatorname{Av}_n(\text{12--34})$ denote the set of permutations of length $n$ avoiding the vincular pattern $\text{12--34}$, and let $A$, $\mu$ and $\beta$ be constants. St…

Asymptotic enumeration conjecture. We have

Singhal's conjecture. The limit

The multipartite semiregular factorisation conjecture. If $n\to\infty$ with $2\le m\le n$ and $1\le k=o(m)$, then

Let $s_g$, $\hat n_g$, and $\mathsf{r}_{1.51}$ be the sequences and constant defined in the source, where $g$ tends to infinity. Conjectural asymptotics. The paper gives three succ…

Let $c_n$ be the coefficient sequence for either the $110$-avoiding or the $100$-avoiding ascent sequences. For the $100$-avoiding sequence, the paper estimates … with…

Refined asymptotic conjecture. The parameters are conjectured to satisfy

Factorial-growth constant conjecture. The constant is conjectured to be

For each ground-set size, let matroids be counted on an $n$-element ground set, and consider the property of having a free basis. Bansal–Pendavingh free-basis conjecture. Asymptoti…

Let $L_n$ denote the number of Latin squares of order $n$. Eberhard–Manners–Mrazović conjecture. The number of Latin squares satisfies … This conjecture uses maximum-entropy method…