Tootfinder

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps
Peice Hua
https://arxiv.org/abs/2508.05981 https://arxiv.org/pdf/2508.…

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps
We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs $ (G,\mathcal{M}) $, such that $ G $ is a finite 2-group and $ \mathcal{M} $ is a $ G $-arc-transitive map with Euler characteristic not being divisible by 4.

On the Spectral Analysis of the Superpower Graph of the Direct Product of Dihedral Groups
Basit Auyoob Mir, Fouzul Atik
https://arxiv.org/abs/2508.06812 https://

On the Spectral Analysis of the Superpower Graph of the Direct Product of Dihedral Groups
The superpower graph of a finite group $G$, or $\mathcal{S}_G$, is an undirected simple graph whose vertices are the elements of the group $G$, and two distinct vertices $a,b\in G$ are adjacent if and only if the order of one vertex divides the order of the other vertex, which means that either $o(a)|o(b)$ or $o(b)|o(a)$. In this paper, we have investigated the adjacency spectral properties of the superpower graph of the direct product $D_p\times D_p$, where $D_p$ is a dihedral group …

Knot primality: knot Floer homology, metacyclic representations and twisted homology
Samantha Allen, Charles Livingston
https://arxiv.org/abs/2508.08102 https://

Knot primality: knot Floer homology, metacyclic representations and twisted homology
We develop purely algebraic methods for proving that a knot is prime. Our approach uses the Heegaard Floer polynomial in conjunction with classical knot-theoretic methods: cyclic, dihedral, and metacyclic covering spaces. The theory of twisted homology allows us to view these approaches from a unified perspective. Collectively, the primality tests developed here have proved primality for over 99.6% of knots in large families of prime knots, including all prime knots with 15 or fewer crossings.

Electronic Fluctuations and Ionic Dynamics in Molten Silver Iodide
Harender S. Dhattarwal, Richard C. Remsing
https://arxiv.org/abs/2509.08143 https://arxi…

Electronic Fluctuations and Ionic Dynamics in Molten Silver Iodide
Molten salts are high-temperature ionic liquids whose unique combination of strong Coulombic interactions, large polarizabilities, and high ionic conductivities makes them central to energy storage, metallurgy, and nuclear technology. Understanding their delicate balance of Coulomb forces, short-range repulsion, and electronic polarization, particularly regarding the role that electronic fluctuations play in their structure and dynamics, is critical to predictively designing molten salts for ap…

A possibility of describing a sequential gauge symmetry as a part of the dihedral flavor symmetry and its implications
Jae Jun Kim
https://arxiv.org/abs/2510.06155 https://

A possibility of describing a sequential gauge symmetry as a part of the dihedral flavor symmetry and its implications
We present a method in which the dimension-five and -six terms in a sequential gauge symmetry can coexist with that of the dihedral flavor symmetry. We start with the contents in the model proposed in a sequential gauge symmetry, meeting the conditions for the contents to be described in the flavor symmetry, build up the mass matrices and discuss its implications. Given that the breaking of the symmetry only takes place in the dimension-five and -six terms in the mass matrix of the charged ferm…

Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect
Zhao Xu
https://arxiv.org/abs/2509.05968 https://arxiv.org/pdf/250…

Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect
In this paper, we study the second moment for $GL(2)\times GL(2)$ $L$-functions $L(\frac{1}{2},f\times g)$, which leads to a uniform subconvexity bound in the spectral aspect. In particular, if either $f$ or $g$ is a dihedral Maass newform, or if one of them has level $1$, we obtain a Burgess-type bound that is uniform in both $t_f$ and $t_g$, where $t_f$, $t_g$ denote the spectral parameters of $f$, $g$. As an application, we also establish a shrinking result for QUE in the case of dihedral Ma…

Abelian and Dihedral equiangular tight frames of redundancy $2$
Assaf Goldberger, Radel Ben Av, Xuemei Chen, Kasso A. Okoudjou
https://arxiv.org/abs/2509.01753 https://

Abelian and Dihedral equiangular tight frames of redundancy $2$
This paper studies group frames ($G$-frames) where the unitary group representation can be projective. When the group is abelian, for most combinations $N, n$, we show that $ETF(N,n)$ can only exist for genuinely projective group representations. In particular, cyclic-group frames for such parameters do not exist. We also give a characterization of all dihedral tight frames and dihedral $ETF(2n,n)$, using which, we conclude that regular dihedral $ETF(2n,n)$ must be genuinely projective. Followi…

Vertex-reversing maps and almost Sylow-cyclic groups
Cai Heng Li, Luyi Liu, Hanyue Yi
https://arxiv.org/abs/2510.07033 https://arxiv.org/pdf/2510.07033

Vertex-reversing maps and almost Sylow-cyclic groups
A map is \emph{vertex-reversing} if it admits an arc-transitive automorphism group with dihedral vertex stabilizers. This paper classifies solvable vertex-reversing maps whose edge number and Euler characteristic are coprime. The classification establishes that such maps comprise three families: dihedral maps, cyclic covers of dihedral maps, and cyclic covers of $S_4$-maps. Our classification based on an explicit characterization of finite almost Sylow-cyclic groups. While Conder--Potocnik--Ši…

Dihedral groups of square-free order are DCI-groups
Istv\'an Kov\'acs, G\'abor Somlai
https://arxiv.org/abs/2509.02778 https://arxiv.org/pdf/25…

Dihedral groups of square-free order are DCI-groups
A finite group $G$ is a called a DCI-group if any two isomorphic Cayley digraphs of $G$ are also isomorphic via an automorphism of $G$. If $G$ is a non-abelian generalised dihedral DCI-group, then Dobson, Muzychuk, and Spiga proved that $G$ must be a dihedral group of square-free order (Ars Math. Contemp., 2022). In this paper, we prove that the converse statement also holds, i.\,e., all dihedral groups of square-free order are DCI-groups.

Enumerating Cayley digraphs on dihedral groups
Zai Ping Lu, Jia Yin Xie, Jin-Hua Xie
https://arxiv.org/abs/2507.21658 https://arxiv.org/pdf/2507.21658

Enumerating Cayley digraphs on dihedral groups
This paper investigates the enumeration of Cayley digraphs, focusing on counting Cayley digraphs on dihedral groups up to CI-isomorphism. By leveraging the Cauchy-Frobenius Lemma and properties of automorphisms, we derive an explicit formula for the number of non-isomorphic Cayley digraphs on dihedral groups with DCI-property, particularly for the group $\mathrm{D}_{6p}$ with $p>3$ a prime. The enumeration involves detailed analysis of cycle numbers of automorphisms and their actions on the gro…