The Catalan number 1/n+1(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.
Lecture Notes
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