# A Study of Lambda Permutations

## Mentor Information

Sherwin Kouchekian (Department of Mathematics and Statistics)

## Description

Infinite series have been a source of mathematical interest since antiquity. In their 2004 publication, “Creating More Convergent Series” S. Krantz and J. McNeal describe a subset of permutations of the natural numbers that are convergence preserving for any absolutely convergent infinite series while their inverses are not. These permutations are titled “Lambda- Permutations”. We look into the specifics of these permutations, as well as relevant literature and generalizations known about all convergence preserving permutations. Namely, F. W. Levi’s notion of a “bunch” and its relation to preserving of convergence. We generalize an example permutation of Krantz and McNeal, and explore certain specifics of this generalization relating to the “bunch-number”.

A Study of Lambda Permutations

Infinite series have been a source of mathematical interest since antiquity. In their 2004 publication, “Creating More Convergent Series” S. Krantz and J. McNeal describe a subset of permutations of the natural numbers that are convergence preserving for any absolutely convergent infinite series while their inverses are not. These permutations are titled “Lambda- Permutations”. We look into the specifics of these permutations, as well as relevant literature and generalizations known about all convergence preserving permutations. Namely, F. W. Levi’s notion of a “bunch” and its relation to preserving of convergence. We generalize an example permutation of Krantz and McNeal, and explore certain specifics of this generalization relating to the “bunch-number”.