Results 91 to 100 of about 104,175 (189)

A subexponential-time quantum algorithm for the dihedral hidden subgroup problem

, 2003
We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity $O(\exp(C\sqrt{\log N}))$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a hidden reflection ...
Kuperberg, Greg
core   +1 more source

Sequencing the dihedral groups D4k

Discrete Mathematics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Unions of dihedral groups

Semigroup Forum, 1986
By the following simple formula (1) \(\forall x\exists y\) \((x=xyy\), \(y=xyx)\) we characterize semigroups from the title. Considering a local property of their \({\mathcal H}\)-classes we get bands and Boolean groups as extreme cases of semigroups with that property.
openaire   +2 more sources

The Harborth Constant of Dihedral Groups

, 2018
The Harborth constant of a finite group $G$, denoted $\gs(G)$, is the smallest integer $k$ such that the following holds: For $A\subseteq G$ with $|A|=k$, there exists $B\subseteq A$ with $|B|=\exp(G)$ such that the elements of $B$ can be rearranged into a sequence whose product equals $1_G$, the identity element of $G$. The Harborth constant is a well
Balachandran, Niranjan, Mazumdar, Eshita, Zhao, Kevin   +2 more
openaire   +3 more sources

Study of Cayley Digraphs over Polygroups

Mathematics
In this paper we introduce Cayley digraphs associated to finitely generated polygroups, where the vertices correspond to finite products of the generators of polygroups and the edges to multiplication by vertices and generators.
Ali Sanjabi, Morteza Jafarpour, Sarka Hoskova-Mayerova, Hossien Aghabozorgi, Alena Vagaska   +4 more
doaj   +1 more source

Orthomorphisms of dihedral groups

Discrete Mathematics, 1997
An orthomorphism \(\phi\) of a finite group \(G\) is a permutation of \(G\) such that the mapping \(x\mapsto x^{-1}\phi (x)\) is also a permutation. Orthomorphisms \(\phi_1,\phi_2\) of \(G\) are orthogonal if the mapping \(x\mapsto \phi_1(x)^{-1}\phi_2(x)\) is a permutation of \(G.\) Denote by \(\omega (G)\) the maximum cardinality of a set of pairwise
openaire   +1 more source

Sequencing certain dihedral groups

Discrete Mathematics, 1990
A sequencing of a finite group is an ordering of its elements such that the partial products of its nonempty initial segments exhaust all group elements (without repetition). It is shown that at least three-fourths of the dihedral groups are sequenceable.
openaire   +2 more sources

Machine Learning Driven Exploration of Energies and Generalization of Topological Indices for the Fuzzy Conjugate Graph of Dihedral Group

IEEE Access
This study introduces a ground-breaking approach to analyzing dihedral groups through the lens of fuzzy graph theory, significantly enhancing computational efficiency in group theory.
Muhammad Umar Mirza, Rukhshanda Anjum, Adel Fahad Alrasheedi, Jungeun Kim   +3 more
doaj   +1 more source

Action of dihedral groups

, 2013
Let $K$ be any field and $G$ be a finite group. Let $G$ act on the rational function field $K(x_g: \ g \in G)$ by $K$-automorphisms defined by $g \cdot x_h=x_{gh}$ for any $g, \ h \in G$. Denote by $K(G)$ the fixed field $K(x_g: \ g \in G)^G$. Noether's problem asks whether $K(G)$ is rational (=purely transcendental) over $K$.
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Role of Central Arene Rotators and Ag^<b>+</b>, I^<b>+</b>, and PdCl₂ Centers in Hexagonal Macrocycles as Molecular Rotors. [PDF]

Inorg Chem
Litts NP, Lutes AK, Countryman PA, Green EA, Amore AIP, Lyons WC, France NJ, Litts AW, Bowling NP, Scanlon JD.   +9 more
europepmc   +1 more source