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On the Cyclic Symmetry Classes

โœ Scribed by Tin-Yau Tam

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
98 KB
Volume
182
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

The dimensions of the symmetry classes of tensors associated with the product of cyclic subgroups of the symmetric group are explicitly given in terms of the Ramanujan sum. It can also be expressed as the Euler -function and the Mobius ลฝ . function. The results of a paper of Cummings 1976, J. Algebra 40, 401แŽ405 are extended.

๐Ÿ“œ SIMILAR VOLUMES

On the Dimensions of Cyclic Symmetry Cla
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The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $ which is generated by a product of disjoint cycles is explicitly m given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler -function and the Mobius function.

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an orthonormal basis of V. Suppose G is a permutation group of degree m and ลฝ . is an irreducible character of G. We denote by V G the symmetry class of tensors associated with G and . In this article, we discuss the problem of existing ลฝ . U orthogonal bases for V G consisting of symmetrized decom

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A necessary and sufficient condition for the existence of the orthogonal basis of decomposable symmetrized tensors for the symmetry classes of tensors associated with dicyclic group and dihedral group were studied by M. R. Darafsheh and M. R. ลฝ . Pournaki in press, Linear and Multilinear Algebra an

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## Abstract A general dispersion relation for the polariton region of triclinic, optically active crystals is presented.

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## Abstract Cyclic symmetric structures are those that posses a circumferentially periodic geometry, e.g. gear wheels, bladed discs, etc. Accurate prediction of their static and dynamic characteristics is essential to ensure optimum design. An analysis of the entire structure is often prohibitively