Non-crossing partitions for classical reflection groups

摘要: Abstract We introduce analogues of the lattice non-crossing set partitions for classical reflection groups types B and D . The type (first considered by Montenegro in a different guise) turn out to be as well-behaved original partitions, almost well-behaved. In both cases, they are EL-labellable ranked lattices with symmetric chain decompositions (self-dual ), whose rank-generating functions, zeta polynomials, rank-selected numbers have simple closed forms.