n] is equal to the number of derangements in the

symmetric group [S.

Key Words:

Symmetric Group, Character Table and Triangular Group.

The sources of the

symmetric group and the data transmission direction are the same as that of the flow.

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.

n - 1) with the transposition (i, i + 1) and therefore the

symmetric group is

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).

The 16 papers from the latest Osaka conference on Schubert calculus consider such topics as consequences of the Lakshmibai-Sandhya theorems: the ubiquity of permutation patterns in Schubert calculus and related geometry, stable quasi-maps to holomorphic symplectic quotients, tableaux and Eulerian properties of the

symmetric group, generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur P- and Q-functions, and character sheaves on exotic symmetric spaces and Kostka polynomials.

It is well known that there is a natural map from the

symmetric group cohomology to the usual group cohomology

It is well known that the

symmetric group Sn is the Coxeter group of type [A.