27 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…

Converse conjecture. If a dihedral group of order $2n$ has $n=2$ or $n$ odd and square-free, then it is a DCI-group.

Let $L/k$ be a Galois extension of number fields with Galois group isomorphic to the dihedral group $D$, and let $\mathcal{O}_L$ be the ring of integers of $L$. For…

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…

Dihedral group-algebra length conjecture.

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…

Let $X$ be a finite indecomposable cycle set whose permutation group is the dihedral group $D_{2n}$. Its fundamental group at $x\in X$ is … A universal covering of $X$ is a coverin…

Let $D_q$ be a dihedral group acting locally over an algebraically closed field $k$ of characteristic $p>0$. Assume that the KGB obstruction for this action vanishes. Dihedral KGB-…

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…

Support conjecture. $H_p(\rho,\cdot)$ is supported in the convex hull of $\mathcal{D}_2(2p)\rho$.

The intersecting-set dihedrant construction. Then $Dih(n,X,X)$ is a directed strongly regular graph with parameters

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…

Splitting conjecture. In general, this sequence splits, so that

Let $D_{2n}=\langle a,b\mid a^n,b^2,abab\rangle$ be a finite dihedral group. A subset is sum-dominant when its sumset has greater cardinality than its difference set, and differenc…

Let $D_{2n}=\langle a,b\mid a^n,b^2,abab\rangle$ be a dihedral group. A subset is balanced when its sumset and difference set are equal to the whole group; it is sum-dominant when…

Let $G$ be a dihedral group, and let ${\rm P}(G)$ and $\Lambda(G)$ denote its left and right commutator semigroups, respectively. For non-abelian $2q$ groups, the results above est…

Let $K$ be an oriented knot and let $D_p$ be the dihedral group of order $2p$, with $p=2\ell+1$ an odd prime. Let $\alpha\colon\pi_1(X_K)\to D_p$ be an epimorphism. Hirasawa–Murasu…

Let $R$ be a field, let $n$ be a positive integer, and let $W({\rm I}_2^n)$ be the corresponding dihedral group. The characteristic of $R$ is assumed not to divide $n$. Cellularity…

Let $D_{2p}$ be the dihedral group of order $2p$, where $p$ is an odd prime, and let $\beta_{\operatorname{sep}}(D_{2p})$ denote the separating degree bound for this group over a f…