81 problems

Asymptotic extremal covariance conjecture.

For each $n\in\mathbb{N}$, let $W_n$ be the set of permutations of size $n$, let $\operatorname{Simp}_n$ be the set of blockwise simple permutations, and define … where $S_n$ is th…

Let $B(n-1)$ denote the number of $1$-perfect binary codes of length $n-1=2^m-1$, and let $\widetilde K_{\scriptscriptstyle LA}(n)$ be the lower-bound expression satisfying…

Let $M(n)$ denote the number of distinct multinomial coefficients arising from partitions of $n$. Exact-asymptotic-constant conjecture. … The paper explains that this would follow…

Let $M(n)$ denote the number of distinct multinomial coefficients arising from partitions of $n$. Asymptotic-growth conjecture. There exists a positive constant $C$ such that … Thi…

Asymptotic corank-growth conjecture. As $k\to\infty$,

Let $a_p$ and $\alpha_p$ denote the numbers of open and closed plane curves, respectively, with $p$ self-intersections. Let $\gamma=-\frac{1+\sqrt{13}}6$. Asymptotic enumeration co…

Monochromatic NTIL asymptotics. The exact monochromatic no-three-in-line maxima satisfy

Let $\alpha$ be the middle real root of … For odd $n=2m+1$, let $L_m^{\mathrm{fat}}$ and $L_m^{\mathrm{thin}}$ denote the relaxation optima on the fat and thin colour classes, resp…

Let $H$ be an infection rule and let $M_H(n)$ denote its maximum running time. Polynomial-exponent limit conjecture. The limit … exists for every infection rule $H$. The paper does…

Leading-pole cancellation conjecture. The choice

Let $p(3,n)$ denote the number of partitions of a $3\times n$ rectangle into permitted rectangular blocks, as defined in the paper. Asymptotic form conjecture. There exist constant…

For a $1\times n$ strip of stamps, let $M(n)$ be the maximal number of ways to fold the strip over all mountain-valley assignments. Maximal-folding asymptotic conjecture. As…

Let $S(m,k)$ denote the MV assignment with $m$ blocks, each of size $k$, and let $c(S(m,k))$ be its number of foldings. Equal-block asymptotic conjecture. For any fixed $m$ and suf…

Let $FO_{j,k}(n)$ be the number of partitions of $n$ with exactly $j$ parts divisible by $k$, and let $FD_{j,k}(n)$ be the number of partitions of $n$ with exactly $j$ parts appear…

Let $\mathcal P(n)$ be the set of partitions of $n$, let $\mathbf t\in\mathcal P(n)^3$, and let $g(\mathbf t)$ denote the corresponding Kronecker coefficient. Define … Let $F_n$ be…

Let $g\ge2$ and let $\mathbf d$ be a partition of $g-1$. Write $C(\mathbf d)$ for the normalized BGW number associated with $\mathbf d$. Nesting conjecture. … The inequalities asse…

Let $\Sigma$ be an alphabet, let $m\geq 1$, and let $w\in\Sigma^m$ be an $m$-mer. Write $\pi_k(w)$ for the number of objects counted by the paper's minimizer-count function, and le…

Let $\Sigma$ be the underlying alphabet, and for each $k,m$ let $f_{k,m}:[0,1]\to[0,1]$ be the piecewise linear function determined by the points $p(w)=(x,y)$ for $w\in\Sigma^m$, w…

Bessel-integral asymptotic conjecture.

Euclidean-ball asymptotic conjecture.

Simplex asymptotic conjecture.

Let $A267013(d)$ denote the number of non-primonumerophobic digit patterns of length $d$, and let $A164864(d)$ denote the total number of available digit patterns of length $d$. As…

Let the sequence of primes be ordered by increasing value, and call a prime cryptarithmically unique when no other prime has the same multiset of decimal digits. A sequence is asym…

Let $B_r^d$ be the convex body used in the paper, and let $H_r^d$ be the set of lattice polytopes contained in $B_r^d$, with $H_r^d(V/d!\geqslant\mathrm{vol}(B_r^d)-c(r))$ denoting…