Loopless Generation of Schroder Trees

The well-known Schroder numbers have appeared in different combinatorial contexts, including Schroder trees and well-weighted binary trees. The only loopless algorithm for generating Schroder trees actually generated representations for their well-weighted binary tree counterparts. This paper presents the first loopless algorithms for directly generating Schroder tree representations. They use a new loopless algorithm for generating $k$-compositions of $n$ in inverse lexicographic order.