29 problems

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

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

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 $C_n$ 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…

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…

Asymptotic enumeration conjecture. We have

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 $d\in\mathbb{N}_{>0}$, let $F\in\mathbb{N}^d$, and let $N(F)$ denote the number of generalized numerical semigroups with Frobenius element $F$. For $d\ne 5$, define…

Let $H$ be a graph on $m$ edges, let $k$ be a positive integer, let $\delta(H)$ be the minimum degree of $H$, and let $\mathcal{G}_C$ be the graph class defined in the paper. Write…

Let $(\mathbf{f}^{n})_{n \geq 1}$ be a sequence of face degree sequences, and let $(g_n)$ be a sequence such that $v(\mathbf{f}^{n},g_n)\geq 2$ for all $n\geq 1$. Assume that…

Fix $k\geq 3$, let $\pi\in S_k$, and let $a\in\mathbb{Z}^+$. For $n\in\mathbb{Z}^+$ and $I=\{i_1,i_2,\ldots,i_a\}\subseteq[n]$, suppose that … Here $p_{\pi}(I,n)$ counts permutatio…

The asymptotic consecutive-pattern distribution conjecture. For any $k\geq 3$, any $\pi\in S_k$, and any finite $I\subseteq\mathbb{Z}^+$, there are constants…

Xu's conjecture. The minimum, over all groups $R$ of order $r$, of the proportion of inverse-closed subsets $S$ of $R$ such that $\mathop{\Gamma}(R,S)$ is a normal Cayley digraph t…

Powerful 132-avoidance asymptotic conjecture. As $n$ tends to infinity,

Fix $n,k\in\mathbb N$ and a pattern $v\in[k]^*$ using $d>1$ distinct letters. Let $M_r$ be the maximal number of states with $d-1$ loops in a simple path in the automaton…

vanishing-coefficient conjecture. There exist $k,r\in\mathbb N$ and a pattern $v\in[k]^*$ such that $d>1$ and $K_r=0$. In that case, there exist $L_r\in\mathbb N$, $L_r<M_r$, and…

Let $\Sigma=\{0,1\}$, let $\mathcal L_{\mathrm{PN1}}$ be the language of prefix normal words, and let $\textit{ecrit}(n)$ count the extension-critical words in…

The asymptotic enumeration conjecture. Asymptotically almost all representable matroids on $[n]$ have rank in $\{\lfloor n/2\rfloor,\lceil n/2\rceil\}$ and exactly $d(n)-1$ nonbase…

Asymptotic enumeration conjecture. There exist constants $\mu$ and $\gamma$ such that

For each $n$, let $\textit{pnw}(n)$ be the number of prefix normal binary words of length $n$, and let $\textit{crit}(n)$ be the number of extension-critical words of length $n$. P…