Discrete harmonic analysis is the study of functions on domains possessing richer algebraic structure such as the

symmetric group (the group of all permutations), using techniques from representation theory and sperner theory.

Let [f.sub.i-1,j] be the polynomial in (1.2) and [G.sub.w] the Schubert polynomial for a permutation w in the

symmetric group [S.sub.n].

To use the symmetry of an image in the process of creating holograms to reduce the computational complexity, it is necessary to calculate the maximum

symmetric group of the image.

We write [S.sub.n] for the

symmetric group on {1,...,n}.

Key Words:

Symmetric Group, Character Table and Triangular Group.

Rule 2: For any arriving HC request, SHM must first search the wavelengths of the

symmetric group to find one to construct the HC.

The interval structure of the Bruhat order on the

symmetric group is not well understood.

In this paper we study those generic intervals in the Bruhat order of the

symmetric group that are isomorphic to the principal order ideal of a permutation w, and consider when the minimum and maximum elements of those intervals are related by a certain property of their reduced words.

First we determine a

symmetric group of scaling transformations

Among their topics are the probabilistic zeta function, computing covers of Lie algebras, enumerating subgroups of the

symmetric group, groups of minimal order that are not n-power closed, the covering number of small alternating groups, geometric algorithms to resolve Bieberbach groups, the non-abelian tensor product of soluble minimax groups, and the short rewriting systems of finite groups.

In this work, the notion of palindromic permutations and generalized Smarandache palindromic permutations are introduced and studied using the

symmetric group on the set N and this can now be viewed as the study of some palindromes and generalized Smarandache palindromes of numbers.

We also show that the afore-mentioned function g is a generating function for the number of homocyclic permutations in the

symmetric group S(n).