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ON THE PERIODS OF 2STEP GENERAL FIBONACCI SEQUENCES IN DIHEDRAL GROUPS
"... Abstract. In this paper, we investigate the simply periodic cases of 2step general Fibonacci sequences in dihedral groups Dn, and we also find the period of the sequences if the sequences are simply periodic. 1. ..."
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Abstract. In this paper, we investigate the simply periodic cases of 2step general Fibonacci sequences in dihedral groups Dn, and we also find the period of the sequences if the sequences are simply periodic. 1.
CRITICAL GROUPS OF GRAPHS WITH DIHEDRAL ACTIONS
"... In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group Dn. In particular, we show that if the orbits of the Dnaction all have either n or 2n points then the critical group of such a graph can be decomposed in terms of the critical ..."
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In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group Dn. In particular, we show that if the orbits of the Dnaction all have either n or 2n points then the critical group of such a graph can be decomposed in terms of the critical
ConstaDihedral Codes and their Transform Domain Characterization
"... We identify a cocycle on the dihedral group Dn of 2n elements which results in a new class of codes called constadihedral codes. We define a new transform for these codes and then characterize all the constadihedral codes using this new transform. ..."
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We identify a cocycle on the dihedral group Dn of 2n elements which results in a new class of codes called constadihedral codes. We define a new transform for these codes and then characterize all the constadihedral codes using this new transform.
STRONG REFLECTION RIGIDITY OF COXETER SYSTEMS OF DIHEDRAL GROUPS
"... Abstract. In this paper, we study strong rigidity and strong reflection rigidity of Coxeter systems of dihedral groups. We show that the Coxeter system of the dihedral group Dn of order 2n is strongly reflection rigid if and only if n ∈ {2, 3, 4, 6}, and that the dihedral Coxeter group Dn is strongl ..."
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Abstract. In this paper, we study strong rigidity and strong reflection rigidity of Coxeter systems of dihedral groups. We show that the Coxeter system of the dihedral group Dn of order 2n is strongly reflection rigid if and only if n ∈ {2, 3, 4, 6}, and that the dihedral Coxeter group Dn
A subexponentialtime quantum algorithm for the dihedral hidden subgroup problem
, 2003
"... Abstract. We present a quantum algorithm for the dihedral hidden subgroup problem (DHSP) with time and query complexity 2O(√log N). In this problem an oracle computes a function f on the dihedral group DN which is invariant under a hidden reflection in DN. By contrast, the classical query complexity ..."
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Cited by 77 (0 self)
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Abstract. We present a quantum algorithm for the dihedral hidden subgroup problem (DHSP) with time and query complexity 2O(√log N). In this problem an oracle computes a function f on the dihedral group DN which is invariant under a hidden reflection in DN. By contrast, the classical query
Minimal surfaces in R 3 with dihedral symmetry
 Tohoku Math. J
, 1995
"... We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most 2n+1 ends, and with symmetry group the natural 1 2 Z2 extension of the dihedral group Dn. The ..."
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Cited by 1 (0 self)
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We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most 2n+1 ends, and with symmetry group the natural 1 2 Z2 extension of the dihedral group Dn
Dihedral representations and statistical geometric optics II: Elementary instruments
 J. Modern Optics
, 2006
"... The linear 2dim irreducible representations of the dihedral groups �Dn � are interpreted as classical linear operators of geometrical optics. It is shown that the 2dim irreducible representation of D4 is simply the refractive group described by Campbell [Optom. Vision Sci. 74, 381 (1997)]. The dih ..."
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Cited by 15 (11 self)
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The linear 2dim irreducible representations of the dihedral groups �Dn � are interpreted as classical linear operators of geometrical optics. It is shown that the 2dim irreducible representation of D4 is simply the refractive group described by Campbell [Optom. Vision Sci. 74, 381 (1997
EXTREMAL FIRST DIRICHLET EIGENVALUE OF DOUBLY CONNECTED PLANE DOMAINS AND DIHEDRAL SYMMETRY
, 705
"... Abstract. We deal with the following eigenvalue optimization problem: Given a bounded domain D ⊂ R 2, how to place an obstacle B of fixed shape within D so as to maximize or minimize the fundamental eigenvalue λ1 of the Dirichlet Laplacian on D \ B. This means that we want to extremize the function ..."
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ρ ↦ → λ1(D \ ρ(B)), where ρ runs over the set of rigid motions such that ρ(B) ⊂ D. We answer this problem in the case where both D and B are invariant under the action of a dihedral group Dn, n ≥ 2, and where the distance from the origin to the boundary is monotonous as a function of the argument
On the Conjugacy Classes, Centers and Representation of the Groups Sn and Dn
"... Abstract: The desire in this paper is to critically examine the properties of the elements of the symmetric group Sn and the dihedral group Dn. It has always been a difficult task in determining the behaviors of reflections and rotational symmetries in these symmetry groups and how much information ..."
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Abstract: The desire in this paper is to critically examine the properties of the elements of the symmetric group Sn and the dihedral group Dn. It has always been a difficult task in determining the behaviors of reflections and rotational symmetries in these symmetry groups and how much information
GROUP ACTIONS
"... The symmetric groups Sn, alternating groups An, and (for n ≥ 3) dihedral groups Dn behave, by their very definition, as permutations on certain sets. The groups Sn and An both permute the set {1, 2,..., n} and Dn can be considered as a group of permutations of a regular ngon, or even just of its n ..."
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The symmetric groups Sn, alternating groups An, and (for n ≥ 3) dihedral groups Dn behave, by their very definition, as permutations on certain sets. The groups Sn and An both permute the set {1, 2,..., n} and Dn can be considered as a group of permutations of a regular ngon, or even just of its n
Results 1  10
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1,952