Noncrossing partitions
A partition of \(\{1,\ldots,n\}\) is noncrossing if whenever \(1\leq a < b < c < d \leq n\) and \(a,c\) are in the same class and \(b,d\) are in the same class, then the two classes coincide. The enumerative study of noncrossing partitions was originated by G. Kreweras in his seminal 1972 paper; see \textit{G. Kreweras} [Discrete Math. 1, 333-350 (1972; Zbl 0231.05014)]. Meanwhile it turned out that the lattice of noncrossing partitions has a wide interaction with algebraic, geometric combinatorics, probability measures, mathematical biology, etc. This long paper gives a detailed survey on theoretical results on noncrossing partitions as well as its applications on different topics.
scientific article; zbMATH DE number 1453362