We use Young tableaux and Young symmetrizers to classify the irreducible representations over C of the symmetric group on n letters, Sn. We establish an isomorphism between a ring of all representations of finite symmetric groups and the ring of symmetric functions, and, as a corollary, prove the Frobenius formula for the characters of representations of Sn. We use the theory thus developed to ...

A representation of the eld GF (2 n) for various values of n is described, where the eld elements are palindromic polynomials, and the eld operations are polynomial addition and multiplication in the ring of polynomials modulo x 2n+1 ?1. This representation can be shown to be equivalent to a eld representation of Type-II optimal normal bases. As such, the suggested palindromic representation in...

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topologica...

The traditional strategy performed by Information Retrieval (IR) systems is ranked keyword search: For a given query, a list of documents, ordered by relevance, is returned. Relevance computation is primarily driven by a basic string-matching operation. To date, several attempts have been made to deviate from the traditional keyword search paradigm, often by introducing some techniques to captu...

The Burau representation is a natural action of the braid group Bn on the free Z[t; t−1]{module of rank n−1. It is a longstanding open problem to determine for which values of n this representation is faithful. It is known to be faithful for n = 3. Moody has shown that it is not faithful for n 9 and Long and Paton improved on Moody’s techniques to bring this down to n 6. Their construction uses...

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

Let Tn be the space of fully-grown n-trees and let Vn and V ′ n be the representations of the symmetric groups n and n+1 respectively on the unique non-vanishing reduced integral homology group of this space. Starting from combinatorial descriptions of Vn and V ′ n , we establish a short exact sequence of Z n+1-modules, giving a description of V ′ n in terms of Vn and Vn+1. This short exact seq...

We study two subposets of the partition lattice obtained by restricting block sizes. The rst consists of set partitions of f1; : : : ; ng with block size at most k; for k n ? 2: We show that the order complex has the homotopy type of a wedge of spheres, in the cases 2k + 2 n and n = 3k + 2: For 2k + 2 > n; the posets in fact have the same S n?1-homotopy type as the order complex of n?1 ; and th...

supposing the reciprocity of relations between society and media, it is logical to investigate the social changes of women’s identity through inspecting the changes in women’s identity representation in media (particularly cinema). this paper aims to analyze the mutual effects of predominant social affairs of after-islamic revolution of iran on the manner of women’s representation in iran’s cin...

The cluster representation matrices have already been successfully used to enumerate close-packed vacancy clusters in all single-lattice crystals [I, 2]. Point defect clusters in double-lattice crystals may have identical geometry but are distinct due to unique atomic postions enclosing them. The method of representation matrices is extended to make it applicable to represent and enumerate ...