Dihedral group ≈ Dihedral group
View article
Theta, time reversal and temperature Open
SU(N ) gauge theory is time reversal invariant at θ = 0 and θ = π. We show that at θ = π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It…
View article
Digital quantum simulation of lattice gauge theories in three spatial dimensions Open
In the present work, we propose a scheme for digital formulation of lattice\ngauge theories with dynamical fermions in 3+1 dimensions. All interactions are\nobtained as a stroboscopic sequence of two-body interactions with an auxiliary\nsy…
View article
Relation Embedding with Dihedral Group in Knowledge Graph Open
Link prediction is critical for the application of incomplete knowledge graph\n(KG) in the downstream tasks. As a family of effective approaches for link\npredictions, embedding methods try to learn low-rank representations for both\nentit…
View article
On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation Open
This paper explores the structure groups G ( X , r ) of finite non-degenerate set-theoretic solutions ( X , r ) to the Yang–Baxter equation. Namely, we construct a finite quotient $\overline {G}_{(X,r)}$ of G ( X , r ) , generalizing the C…
View article
Primitive quantum gates for dihedral gauge theories Open
We describe the simulation of dihedral gauge theories on digital quantum\ncomputers. The nonabelian discrete gauge group $D_N$ -- the dihedral group --\nserves as an approximation to $U(1)\\times\\mathbb{Z}_2$ lattice gauge theory. In\nord…
View article
Codimension-2 defects and higher symmetries in (3+1)D topological phases Open
(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these def…
View article
Spectrum and L-spectrum of the power graph and its main supergraph for certain finite groups Open
Let G be a finite group. The power graph P(G) and its main supergraph S(G) are two simple graphs with the same vertex set G. Two elements x,y ? G are adjacent in the power graph if and only if one is a power of the other. They are joined i…
View article
The Connection between the PQ Penny Flip Game and the Dihedral Groups Open
This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and its possible extensions. In this paper, it is shown that the PQ penny flip game can be associated, in a precise way, with …
View article
Stringy N = (2, 2) holography for AdS3 Open
We propose a class of AdS3/CFT2 dualities with N = (2, 2) supersymmetry. These dualities relate string theory on AdS3×(S3×T4)/G to marginal deformations of the symmetric product orbifold of T4/G, where G is a dihedral group. We demonstrate…
View article
Strong accessibility for finitely presented groups Open
A hierarchy of a group is a rooted tree of groups obtained by iteratively passing to vertex groups of graphs of groups decompositions. We define a (relative) slender JSJ hierarchy for (almost) finitely presented groups and show that it is …
View article
Some characterizatsion of coprime graph of dihedral group D <sub>2n </sub> Open
The Coprime graph of group G denoted Γ G is a graph with vertices is an element of G, and two distinct vertices are adjacent when its order relative prime. In 2020, Gazir et al. give some characterizations of Γ D 2 n for n a prime power. T…
View article
Two-color Soergel calculus and simple transitive 2-representations Open
In this paper we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of …
View article
The Power Graph of a Dihedral Group Open
Graph theory is one of the topics in mathematics that is quite interesting to study because it is applicable and can be combined with other mathematical topics such as group theory. The combination of graph theory and group theory is that …
View article
An Efficient Public Key Cryptosystem Based on Dihedral Group and Quantum Spin States Open
The enciphering schemes based on medium transformations by following the strict guidelines are almost used everywhere. We have developed the structure to simulate the digital data with quantum spin states rather than following or creating …
View article
On the Spectra of Commuting and Non Commuting Graph on Dihedral Group Open
Study about spectra of graph has became interesting work as well as study about commuting and non commuting graph of a group or a ring. But the study about spectra of commuting and non commuting graph of dihedral group has not been done ye…
View article
ALGEBRAS OF GENERALIZED DIHEDRAL TYPE Open
We provide a complete classification of all algebras of generalized dihedral type, which are natural generalizations of algebras which occurred in the study of blocks of group algebras with dihedral defect groups. This gives a description …
View article
A Finite Presentation of CNOT-Dihedral Operators Open
We give a finite presentation by generators and relations of the unitary\noperators expressible over the {CNOT, T, X} gate set, also known as\nCNOT-dihedral operators. To this end, we introduce a notion of normal form for\nCNOT-dihedral ci…
View article
Palindromic subshifts and simple periodic groups of intermediate growth Open
We describe a new class of groups of Burnside type, giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group…
View article
The Clique Numbers and Chromatic Numbers of The Coprime Graph of a Dihedral Group Open
The graph has many properties and characterizations. One interesting topic to discuss is the clique numbers and chromatic numbers. This research will determine the clique numbers and chromatic numbers of the coprime graph of the dihedral g…
View article
The Intersection Graph of a Dihedral Group Open
The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i \cap H_j \neq {e} . Th…
View article
Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case Open
Recently, perfect state transfer (PST for short) on graphs has attracted great attention due to their applications in quantum information processing and quantum computations. Many constructions and results have been established through var…
View article
Neighbors Degree Sum Energy of Commuting and Non-Commuting Graphs for Dihedral Groups Open
The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacen…
View article
Dihedral groups are of schottky type Open
We show that a dihedral group H of conforma! automorphisms of a closed Riemann surface S can be lifted for a suitable Schottky uniformization of S. In particular, this implies the existence of a suitable symplectic homology basis of S for …
View article
Inductive Approach to Cartan's Moving Frame Method with Applications to Classical Invariant Theory Open
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an equivaria…
View article
Topological indices of non-commuting graph of dihedral groups Open
Assume is a non-abelian group A dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. The non-commuting graph of denoted by is the graph of vertex set whose vertices are non-central eleme…
View article
DEGREE EXPONENT SUM ENERGY OF COMMUTING GRAPH FOR DIHEDRAL GROUPS Open
For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. This graph is known as the commuting graph of G o…
View article
Dihedral symmetries of gauge theories from dual Calabi-Yau threefolds Open
Recent studies (arXiv:1610.07916, arXiv:1711.07921, arXiv:1807.00186) of\nsix-dimensional supersymmetric gauge theories that are engineered by a class of\ntoric Calabi-Yau threefolds $X_{N,M}$, have uncovered a vast web of dualities.\nIn t…
View article
The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group Open
Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is …
View article
Cyclotomic Aperiodic Substitution Tilings Open
The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the 2 n -th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Su…
View article
On the parametrized Tate construction and two theories of real $p$-cyclotomic spectra Open
We give a new formula for $p$-typical real topological cyclic homology that refines the fiber sequence formula discovered by Nikolaus and Scholze for $p$-typical topological cyclic homology to one involving genuine $C_2$-spectra. To accomp…