A note on generating binary trees inA-order andB-order

We introduce in this paper the P-sequences which are integer sequences characterizing binary trees and generating lexicographically all the binary trees in -order. We compute the rank of a P-sequence by a direct formula and not by an algorithm. Furthermore, we introduce the L-sequences which generate directly and lexicographically all the binary trees on A -order, also called natural order. Ranking and unranking algorithms are provided.