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Disposition Polynomials and Plane Trees
disposition disposition polynomial plane tree Prüfer correspondence
2014/6/3
We define the disposition polynomial Rm(x1, x2,..., xn) as ∏k=0m-1(x1 + x2 + ... + xn + k). When m=n-1, this polynomial becomes the generating function of plane trees with respect to the number of you...
The Butterfly Decomposition of Plane Trees
Plane tree doubly rooted plane tree chains in plane trees k-colored plane tree butterfly decomposition Dyck path Schroder path
2014/6/3
We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the butterfly decomposi...
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
plane tree Dyck path 2-Motzkin path Catalan number involution
2014/6/3
The problem of counting plane trees with n edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity wa...
A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees with a given number of old leave...