How to recover a permutation group amidst errors

TL;DR

This paper introduces methods to recover permutation groups from error-prone samples modeled as mixtures of uniform distributions, with applications to numerical monodromy group computations.

Contribution

It presents novel algorithms for recovering permutation groups from noisy data, advancing techniques in group recovery under sampling errors.

Findings

Effective algorithms for group recovery from mixed distributions

Improved understanding of monodromy group computation with errors

Robustness of methods in error-prone sampling scenarios

Abstract

We consider the problem of recovering a permutation group $G \leq S_n$ from an error-prone sampling process $X$. We model $X$ as an $S_n$-valued random variable, defined as a mixture of the uniform distributions on $G$ and $S_n$ . Our suite of tools recovers properties of $G$ from $X$ and bolsters our main method for recovering $G$ itself. Our algorithms are motivated by the numerical computation of monodromy groups, a setting where such error-prone sampling procedures occur organically.