Demazure Product of Permutations and Hopping

The Demazure product (also called the 0-Hecke product or greedy product) is an associative operation on Coxeter groups with interesting properties and important applications. In this paper, we study permutation groups and present a way to compute the Demazure product of two permutations using only their one-line notation and not relying on reduced words. The algorithm starts from their usual product and then applies a new operator, which we call the hopping operator. We also give an analogous result for the group of signed permutations.