Reflection ordering on the group G(m,p,n)

In our previous paper [J.Y. Shi, Formula for the reflection length of elements in the group G(m,p,n), J. Algebra 316 (1) (2007) 284–296], we get a closed formula for the reflection length functions on the reflection group G(m,p,n) with p∈[n] and p|m. In the present paper, we introduce a partial ordering, called reflection ordering, on the elements of G(m,p,n). By applying this formula, we give an explicit description for the reflection ordering on the groups Sn and G(m,1,n), m>1.