Discrete Tomography: Magic Numbers for N-Fold Symmetry

Multiple planar coincidences with N-fold symmetry

Planar coincidence site lattices and modules with N -fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results ...

Permutation symmetry and magic numbers of few-electron systems

Based upon the theory of permutation symmetry and rotation transformation, a powerful method is established to analyse the wavefunctions of identical particles . Applying this method to the two dimensional systems of a few interacting electrons confined by parabolic potential, a simple explanation for the origin of magic numbers is presented. PACS: 73.20.Dx, 71.10.+x, 72.15.Rn, 71.45.-d Typeset...

n-fold Commutative Hyper K-ideals

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

Bravais colourings of planar modules with N -fold symmetry

The first step in investigating colour symmetries for periodic and aperiodic systems is the determination of all colouring schemes that are compatible with the symmetry group of the underlying structure, or with a subgroup of it. For an important class of colourings of planar structures, this mainly combinatorial question can be addressed with methods of algebraic number theory. We present the ...

Magic Numbers in Protein Structures.