Characters of wreath products and some applications to representation theory and combinatorics

The salient point arising out of a consideration of some seemingly independent topics in representation theory, combinatorics and the theory of numerical polynomials turns out to be a result involving characters of representations of wreath products. The topics are: symmetrized inner products of representations, irreducible characters of wreath products, Frobenius' formula for the irreducible ordinary characters of symmetric groups, the Pólya-Redfield theory of enumeration under group action in combinatorics and results of Rudvalis and Snapper that certain polynomials arising from generalized cycleindices of permutation groups are numerical.     

Zur modularen Darstellungstheorie symmetrischer und alternierender Gruppen II

Ohne Zusammenfassung     

Group Actions, Double Cosets, and Homomorphisms: Unifying Concepts for the Constructive Theory of Discrete Structures

In the present paper we describe the use of group actions, double cosets and homomorphisms in the constructive theory of discrete structures, as we found it useful from both a theoretical and a practical point of view. By means of examples we should like to demonstrate that these methods are useful both as unifying principles and as efficient methods for applications.     

Effect of montmorillonite on polypropylene crystallization

The effect of additions of pure and modified montmorrilonite on the polypropylene crystallization rate was studied within the framework of Avrami model. In the presence of these fillers in amounts of 2.5–5.0 wt %, both the crystallization rate and the degree of crystallinity increase, and at the content of these fillers increased to 10% and higher values these parameters decrease. Introduction of fillers enhances the mechanical properties of polypropylene, which allows the developed material to be recommended for the production of packaging film.