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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...
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...
Regression Trees for Longitudinal and Multiresponse Data
CART,decision tree generalized estimating equation linear mixed effect smodel lowess missing values recursive partitioning selection bias
2012/11/22
Previous algorithms for constructing regression tree models for longitudinal and multiresponse data have mostly followed the CART approach. Consequently, they inherit the same selection biases and com...
Extremal values on the eccentric distance sum of trees
Eccentric distance sum Domination number Leaves Bipartition
2012/7/11
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
The shifted wave equation on Damek--Ricci spaces and on homogeneous trees
Abel transform Damek–Ricci space homogeneous tree Huygens’ principle hyperbolic space wave equation wave propagation
2012/6/27
We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar an...
Single--crossover recombination and ancestral recombination trees
population genetics recombination segmentation process ancestral trees
2012/6/21
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the...
Schrodinger Equation on homogeneous trees
homogeneous tree nonlinear Schrodinger equation dispersive estimate Strichartz estimate scattering
2012/6/21
Let T be a homogeneous tree and L the Laplace operator on T. We consider the semilinear Schrodinger equation associated to L with a power-like nonlinearity F of degree d. We first obtain dispersive es...
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symme...
A multivariate hook formula for labelled trees
hook formula tree enumeration representation theory of symmetric groups finite difference operators multivariate Lagrange inversion
2012/5/24
Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, which involves r para...
Absolutely symmetric trees and complexity of natural number
Absolutely symmetric trees complexity of natural number Combinatorics
2012/5/24
We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a co...
Galton-Watson trees with vanishing martingale limit
Conditioning principle large deviations micro-canonical distribution sharp thresholds branching entropic repulsion
2012/4/16
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, agrees up to generation $K$ with a regular $\mu$-ary tree, where $\mu$ is the essential mini...
Amenable, transitive and faithful actions of groups acting on trees
Amenable transitive faithful actions groups trees
2012/3/1
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such...
Abstract: Extending Furstenberg's ergodic theoretic proof for Szemer\'edi's theorem on arithmetic progressions, Furstenberg and Weiss (2003) proved the following qualitative result. For every d and k,...
Dissimilarity maps on trees and the representation theory of $GL_n(\C)$
Dissimilarity maps trees the representation theory Algebraic Geometry
2011/9/14
Abstract: We revisit the representation theory in type $A$used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a di...
Intervals of balanced binary trees in the Tamari lattice
balanced binary tree Tamari lattice poset grammar generating series fixed-point functional equation
2011/9/14
Abstract: We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T, T'] where T and T' are balanced binary trees are isomorphic as ...