14 problems

Let $n\geq 3$ be an integer, and let … be the dihedral group of order $2n$. An MSTD subset is a subset with more distinct pairwise sums than distinct pairwise differences, while an…

Conjugation quandle detection conjecture. The collection of all conjugation quandles over all dihedral groups is able to detect causality across $(2+1)$ globally hyperbolic spaceti…

Stabilizer conjecture. The stabilizer of $W_l'$ is always either

Let $D_n$ be the dihedral group, with order-$n$ cyclic subgroup generated by the usual rotation. Let $S$ be a generating set composed of three involutions, none of which belongs to…

Let $D_n$ be the dihedral subgroup of the symmetric group on $n$ letters, and let $D$ denote the union of the groups $D_n$. For a set $P$ of classical patterns, write…

Jin–Tan's conjecture. Every connected $2$-distance transitive dihedrant either is a known $2$-arc transitive dihedrant, is isomorphic to $\mathsf{K}_{m[b]}$ for some $m\geq 3$ and…

Generalized dihedral MSTD–MDTS conjecture. There are more MSTD subsets of $D$ than MDTS subsets of $D$.

Fixed-size MSTD–MDTS conjecture. For every integer $n\geq 3$ and every $m\leq 2n$, the collection $\mathcal S_{2n,m}$ has at least as many MSTD sets as MDTS sets.

Let $X$ be an indecomposable solution of the Yang–Baxter equation whose permutation group is isomorphic to the dihedral group $D_{2n}$. Dihedral size conjecture. Then … For an inde…

Let $n$ be a positive integer and let $\mathrm{D}_{2n}$ be the dihedral group of order $2n$. A finite group is a DCI-group if every Cayley digraph on it is a CI-digraph, and a CI-g…

Let $D_{2n}=\langle s,r\mid s^2=r^n=1,\ srs=r^{-1}\rangle$ be a dihedral group and let $\mathbb{Z}_{2n}$ be the cyclic group of the same order. Suppose that … is an order-dividing…

Let $D_n$ be a dihedral group, let $S$ be a generating set, and let $l_S(g)$ denote the length of an element $g$ with respect to $S$. For an integer $m$ with $0<m<n$, consider the…

Let $D_n$ be a dihedral group with an order $n$ cyclic subgroup, and let $S$ be a generating set composed of three involutions, none of which belongs to that cyclic subgroup. Write…

Let $K$ be a knot and let … be a non-abelian linear representation, where $D_\ell$ is the dihedral group of order $2\ell$ and $\ell$ is an odd prime. Hirasawa–Murasugi conjecture.…