... Crossing, nesting and alignments of two edges The numbers of crossings, nestings and alignments of two edges in π will be denoted bycr(π), ne(π)andal(π), respectively. For the partition π in Figure ... crossings and nestings of two edges in matchings, preprint, math.CO/0510676, 2005.[9] C. Krattenthaler, Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes, preprint, math.CO/0503012, ... an involution on set partitions which keeps track of the numbers of crossings, nestings and alignments of two edges. We derive then the symmetricdistribution of the numbers of crossings and nestings...