Raney paths and a combinatorial relationship between rooted nonseparable planar maps and two-stack-sortable permutations

Abstract

An encoding of the set of two-stack-sortable permutations (T L L) in terms of lattice paths and ordered lists of strings is obtained. These lattice paths are called Raney paths. The encoding yields combinatorial decompositions for two complementary subsets of T L L, which are the analogues of previously known decompositions for the set of nonseparable rooted planar maps (N L). This provides a combinatorial relationship between T L L and N L, and, hence, a bijection is determined between these sets that is different, simpler, and more refined than the previously known bijection. © 1996 Academic Press, Inc.