Generating functions for the number of commuting m-tuples in the symmetric groups are obtained. We define a natural sequence of “orbifold Euler characteristics” for a finite group G acting on a manifold X . Our definition generalizes the ordinary Euler characteristic of X/G and the string-theoretic orbifold Euler characteristic. Our formulae for commuting m-tuples underlie formulas that general...

This work examines the problem to describe an efficient algorithm for obtaining n × n Sudoku matrices. For this purpose, we define the concepts of n×n Πn-matrix and disjoint Πn-matrices. The article, using the set-theoretical approach, describes an algorithm for obtaining n-tuples of n× n mutually disjoint Πn matrices. We show that in input n 2 mutually disjoint Πn matrices, it is not difficult...

In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for N-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar multipliers of a vector-valued reproducing kernel Hilbert space. We use these to further develop a quantized function theory for various domains that extends and u...

Consider the space Hom(Z n , G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingulariza-tion of the generic component of Hom(Z n , G), which allows us to derive formulas for its singular and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the ...

In this paper, using the recently discovered notion of S-spectrum, we prove spectral theorem for a bounded or unbounded normal operator on Clifford module (i.e., two-sided Hilbert over algebra based units that all square to be $$-1$$ ). Moreover, establish existence Borel functional calculus operators module. Towards end, have developed many results analysis, theory, integration theory and meas...

We prove the `p-spectral radius formula for n-tuples of commuting Banach algebra elements. This generalizes results of [6], [7] and [10]. Let A be a Banach algebra with the unit element denoted by 1. Let a = (a1, . . . , an) be an n-tuple of elements of A. Denote by σ(a) the Harte spectrum of a, i.e. λ = (λ1, . . . , λn) / ∈ σ(a) if and only if there exist u1, . . . , un, v1, . . . , vn ∈ A suc...