Generating Tuples of Free Products

Orbifold Euler Characteristics and the Number of Commuting M-tuples in the Symmetric Groups

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...

Adjacencies in Words

Based Based on on two two inversion inversion formulas formulas for for enumerating enumerating words words in in the the free free monoid monoid by by adjacencies, adjacencies, we we present present a a new new approach approach to to a a class class of of permutation permutation problems problems having having Eulerian-type Eulerian-type generating generating functions. functions. We We also ...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

The Finitary Andrews-Curtis Conjecture

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexam...

Operators Cauchy Dual to 2-hyperexpansive Operators: The Multivariable Case

Abstract. As a natural outgrowth of the work done in [18] and [21], we introduce an abstract framework to study generating m-tuples, and use it to analyze hypercontractivity and hyperexpansivity in several variables. These two notions encompass (joint) hyponormality and subnormality, as well as toral and spherical isometric-ness; for instance, the Drury-Arveson 2-shift is a spherical complete h...