Noncrossing Partition

Noncrossing Partition

In combinatorial mathematics, the topic of noncrossing partitions has assumed some importance because of (among other things) its application to the theory of free probability. The set of all noncrossing partitions is one of many sets enumerated by the Catalan numbers. The number of noncrossing partitions of an n-element set with k blocks is found in the Narayana number triangle.