Noncrossing partitions
type: Item
instance of: scholarly article
title: Noncrossing partitions
zbMATH Open document ID: 0959.05009
DOI: 10.1016/S0012-365X(99)00273-3
author: Rodica Simion
published in: Discrete Mathematics
publication date: 2001-04-20T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 92B99
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 1453362
zbMATH Keywords: noncrossing partition
zbMATH Keywords: algebraic combinatorics
zbMATH Keywords: topology
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
Wikidata QID: Q59649902
full work available at URL: s0012-365x(99)00273-3
OpenAlex ID: W2913109207
DBLP publication ID: journals/dm/Simion00
description: scientific article; zbMATH DE number 1453362