Reflection ordering on the groupG(m,m,n)

Abstract

Communicated by M. Broue a b s t r a c t In the paper Shi (2008) [13], we introduced a partial ordering, called the reflection ordering, on the elements of G(m, p, n) and described such an ordering on the groups G(m, 1, n), m ⩾ 1. In the present paper, we describe the reflection ordering on the group G(m, m, n). As a by-product, we obtain a formula for the enumeration of a certain subset in the symmetric group S n , which is of independent combinatorial interest.