Output details

Decompositions and statistics for β(1,0)-trees and nonseparable permutations

<12>Significance is the deep structural connection between pattern avoiding permutations on one hand and certain trees and the much studied planar maps on the other. Presents an intriguing involution on the trees (whose fixed points were later described by Kitaev and de Mier in arXiv:1210.2618), whose action on the maps is yet to be understood. The paper also introduced a powerful algorithm for finding all possible equidistributions of multi-statistics on two sets of combinatorial objects. That algorithm was used to classify all known bijections between 321- and 132-avoiding permutations, exposing numerous redundancies in the literature (Sém. Lothar. Combin. B60d, 2008).