Laboratoire d’Informatique Algorithmique: Fondements et Applications (LIAFA), University of Paris 7, France

The Catalan number \(\frac{1}{n+1}\binom{2n}{n}\) is perhaps the most frequently occurred number in combinatorics. Richard Stanley has collected more than 170 combinatorial objects counted by the Catalan number. Noncrossing partition, which has received great attention recently, is one of these, so called, Catalan objects. Noncrossing partitions are generalized to each finite Coxeter group. In this talk, we will interpret noncrossing partitions of type B in terms of noncrossing partitions of type A. As applications, we can prove interesting properties of noncrossing partitions of type B.