Symmetric partitions and pairings
Volume 86 / 2000
                    
                    
                        Colloquium Mathematicum 86 (2000), 93-101                    
                                        
                        DOI: 10.4064/cm-86-1-93-101                    
                                    
                                                Abstract
The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.
 
             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                         
                                                            