搜索结果: 1-14 共查到“应用数学 Trees”相关记录14条 . 查询时间(0.078 秒)
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We show that the set of occupied sites for this mode...
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...
We give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in the study of the PAC-Bayesian machi...
On Han's Hook Length Formulas for Trees
hook length formula k-ary tree bijection staircase labeling
2014/6/3
Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han’s formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic ...
Fires on trees
Fires on trees math
2010/11/15
We consider random dynamics on the edges of a uniform Cayley tree with $n$ vertices, in which edges are either inflammable, fireproof, or burt. Every inflammable edge is replaced by a fireproof edge a...
Spectral characterization of a specific class of trees
Spectral characterization specific class of trees
2010/11/9
In this paper, it is shown that the graph $T_4(p,q,r)$ is determined by its Laplacian spectrum and there are no two non-isomorphic such graphs which are cospectral with respect to adjacency spectrum. ...
An upper bound for the Hosoya index of trees
Hosoya index of graphs tree eigenvalue of graphs
2010/9/13
The Hosoya index of a graph G is defined as the sum of all the numbers of k - matchings (k ≥ 0) in G. An upper bound for the Hosoya index of trees is presented in this note.
In this paper, we find recursive relations t(Ln) = 4t(Ln−1)−t(Ln−2), t(Fn) = 3t(Fn−1) − t(Fn−2), and t(Wn) = t(Wn−1) + t(Fn) + t(Fn−1), for determining ...
Hook Length Formulas for Trees by Han's Expansion
hook length formulas for trees k-ary trees planes trees labeled trees
2014/6/3
Recently Han obtained a general formula for the weight function corresponding to the expansion of a series in terms of hook lengths of binary trees. In this paper, we present weight function formulas ...
Formulas for the number of spanning trees in a fan
Graph theory spanning trees enumeration
2010/9/10
Let Pn be a simple path on n vertices. An n-fan is a simple graph G formed from a path Pn by adding a vertex adjacent to every vertex of Pn. In this work we denote n-fan by Fn+1 and derive the explici...
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...
We give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a problem proposed by...
