17 problems

Duong–author sharpness conjecture. These bounds are sharp for all $k\ge 1$: the lower equality case is represented by $T_{3k,3k,3k+1}$, and the upper equality case by…

Let $P$ be the Promislow group. For each positive integer $n$, let $D(n)$ denote the least word-radius of a non-unique-product $n$-element subset of $P$, when such subsets exist. P…

A position in $4 \times n$ Chomp is a quadruple $(a,b,c,d)$ of non-negative integers with $a\geq b\geq c\geq d\geq 0$; a P-position is a position from which the previous player has…

Let $p$ and $q$ be coprime integers with $q$ odd. For the periodic problem $\Sigma(p/q)$, let $\gamma_k(p/q)$ denote the length of the gap with label $k$. Gap-decay and extremal-fr…

Let $m$ be an odd integer with $m\geq 5$, and let $W\in\mathbb{Z}_2*\mathbb{Z}_4$. Let $\tau_W(\lambda)$ denote the trace polynomial associated with $W$. The trace-polynomial nonex…

Consider singularity types with $(p_1,p_2,p_3,p_4)=(2,3,5,n)$, subject to the conditions and obstruction techniques used in the paper. Finiteness conjecture. Only finitely many suc…

Iraids et al.'s conjecture.

Keras-overhead conjecture. The overhead in calling the Keras function texttt{model.predict} is the dominant cost in network evaluation, especially when the number of moments to be…

Let $B_3$ be the three-strand braid group, let $\Sigma_3^{\scriptstyle *}$ denote its dual generating set, and let $\mathcal{S}(B_3,\Sigma_3^{\scriptstyle *})$ and…

Algebraicity conjecture. All spherical codes in the Current Status of Unknown Parameters section are algebraic; in particular, their associated defining polynomials have finite deg…

Non-uniformity conjecture. For $n>2$, as $2d$ grows, the distribution of the $h$-ratio over lattices does not converge to the uniform distribution.

Let $\operatorname{AK}(3)$ denote the specified Andrews–Kurtis presentation, and consider presentations that are $\operatorname{AK}(3)$-equivalent. A normal form is a representativ…

Let $t_{2}(2,q)$ be the smallest size of a complete arc in $\mathrm{PG}(2,q)$, and let the bounds denoted in the source by … be the explicit upper bounds obtained from the computed…

Largest-exception conjecture. The integer $149{,}894$ is the largest exception to the equations in Theorem; equivalently, those equations hold for every $n>149{,}894$.

Let a flat $\varepsilon$-knot be a knot diagram considered up to flat isotopy, and let $c$ denote its number of crossings. Consider the normal forms produced by the experiments wit…

Let $a_\rho^{(3)}$ be the coefficients in the monomial expansion of $g_3$. Kerov's numerical conjecture. For $k=3$, the values of $500\cdot5!\cdot7!\,a_\rho^{(3)}$ are given by the…

Let $c_\rho^{(3)}$ be the coefficients in the monomial expansion of $f_3$. Goulden–Rattan's numerical conjecture. For $k=3$, the values of $2\cdot 6!\cdot 8!\,c_\rho^{(3)}$ are giv…