Trees, Paths, Animals and Permutations

Wen-jin Woan

Howard University, Washington, DC 20059, U.S.A.

wwoan@fac.howard.edu

Abstract. Full Text PDF

We study the relationships among the combinatorial objects: Trees, Paths, Animals and Permutations. The Catalan sequence counts the rooted plane trees and lattice paths with up-step and down-step. For Motzkin paths we add level-step. We show a bijection between Motzkin paths and directed animals. By labelling the nodes of the rooted plane trees in increasing manner we have a bijection between labelled trees and permutations. We study some subsets of permutations that represent the Eulerian numbers, tan-sec numbers, Stirling numbers, Bell numbers.