Editing Noncrossing partition (section)

[[File:Noncrossing partitions 5.svg|thumb|There are 42 noncrossing and 10 crossing partitions of a 5-element set]]
[[File:Noncrossing partitions 4; Hasse.svg|thumb|The 14 noncrossing partitions of a 4-element set ordered by [[Partition of a set#Refinement of partitions|refinement]] in a [[Hasse diagram]] ]]

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 number of noncrossing partitions of a set of ''n'' elements is the ''n''th [[Catalan number]]. The number of noncrossing partitions of an ''n''-element set with ''k'' blocks is found in the [[Narayana number]] triangle.