# Cycle index sum for non-k-equal configurations

## TL;DR

This paper calculates the cycle index sum of the symmetric group acting on the homology of configuration spaces where no k points are equal, providing new insights into the algebraic structure of these spaces.

## Contribution

It introduces a novel computation of the cycle index sum for non-k-equal configuration spaces, advancing understanding of their symmetric group actions.

## Key findings

- Explicit cycle index sum formulas derived
- Enhanced understanding of symmetric group actions on these spaces
- Potential applications in algebraic topology and combinatorics

## Abstract

We compute the cycle index sum of the symmetric group action on the homology of the configuration spaces of points in a Euclidean space with the condition that no $k$ of them are equal.