Flag weak order on wreath products

TL;DR

This paper introduces a specific generating set for the wreath product of cyclic groups and symmetric groups, leading to a well-structured weak order, and explores its properties.

Contribution

It presents a new generating set for the wreath product that induces a well-behaved weak order, advancing understanding of its combinatorial structure.

Findings

A generating set for $\\ZZ_r \\wr S_n$ is proposed.

Properties of the weak order induced by this set are analyzed.

The resulting order exhibits desirable combinatorial features.

Abstract

A generating set for the wreath product $\ZZ_r \wr S_n$ which leads to a nicely behaved weak order is presented, and properties of the resulting order are studied.