Symmetry Class of Tensors Associated with Certain Groups
نویسنده
چکیده
The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $n which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function. In the following we show some results appeared in [2]. Definition 2.1 Let n1, . . . , np be positive integers and let h be a nonnegative integer. Suppose d1|n1, . . . , dp|np. The generalized Ramanujan sum denoted by S(h;n1, . . . , np; d1, . . . , dp) is defined by
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