Multiresolution analysis on the symmetric group

The theory of matrix-valued multiresolution analysis frames

Supplement to “ Multiresolution analysis on the symmetric group ”

Representations. For the purposes of this paper a representation of G over C is a matrix-valued function ρ : G → Cdρ×dρ such that ρ(x)ρ(y) = ρ(xy) for any x, y ∈ G. We call dρ the order or the dimensionality of ρ. Note that ρ(e) = I for any representation. Two representations ρ1 and ρ2 of the same dimensionality d are said to be equivalent if for some invertible T ∈ Cd×d, ρ1(x) = Tρ2(x)T for an...

Wavelet bi-frames with uniform symmetry for curve multiresolution processing

This paper is about the construction of wavelet bi-frames with each framelets being symmetric. When filter banks are used for surface multiresolution processing, it is required that the corresponding decomposition and reconstruction algorithms, including the algorithms for boundary vertices, have high symmetry which makes it possible to design the corresponding multiresolution algorithms for ex...

Balanced multiresolution for symmetric/antisymmetric filters

Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this article can establish a balanced multiresolution scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced d...

A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS

The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.