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Lamplighters, metabelian groups, and horocyclic products of trees     trees  metabelian groups       font style='font-size:12px;'> 2015/8/26
Bartholdi, Neuhauser and Woess proved that a family of metabelian groups including lamplighters have a striking geometric manifestation as 1-skeleta of horocyclic products of trees. The purpose of thi...
The absence of efficient dual pairs of spanning trees in planar graphs     planar graphs  cells       font style='font-size:12px;'> 2015/8/26
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G* such that T and T* do not intersect. We show that it is not always possible to find T in ...
Groups of automorphisms of trees and their limit sets     Groups  automorphisms  trees  limit sets       font style='font-size:12px;'> 2015/8/26
Let T be a locally finite simplicial tree and let ! ⊂ Aut(T ) be a finitely generated discrete subgroup. We obtain an explicit formula for the critical exponent of the Poincare series associated...
Shrinking Trees     Shrinking Trees       font style='font-size:12px;'> 2015/8/21
Tree-based models provide an alternative to linear models for classification and regression data. They are used primarily for exploratory analysis of complex data or as a diagnostic tool following a l...
Margin trees for high-dimensional classification     Maximum margin classifier  supprt vector machine  decision tree  CART       font style='font-size:12px;'> 2015/8/21
We propose a method for the classification of more than two classes, from high-dimensional features. Our approach is to build a binary decision tree in a top-down manner, using the optimal margin clas...
An elector sits on each vertex of an in nite tree of degree k, and has to decide between two alternatives.At each time step, each elector switches to the opinion of the majority of her neighbors. We a...
STRUCTURAL ANALYSIS OF ARONSZAJN TREES     STRUCTURAL ANALYSIS  ARONSZAJN TREES       font style='font-size:12px;'> 2015/8/17
In this paper I will survey some recent developments in the combinatorics of Aronszajn trees. I will cover work on coherent and Lipschitz trees, the basis problem for uncountable linear orderings, sub...
The Rotor-Router Model on Regular Trees     Rotor-Router Model  Regular Trees       font style='font-size:12px;'> 2015/8/14
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...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES     Hopf algebr  rooted tree  planar binary tree  symmetric group       font style='font-size:12px;'> 2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We give explicit isomorphisms showing that the asso...
We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose...
STRUCTURE OF THE LODAY-RONCO HOPF ALGEBRA OF TREES     Hopf algebra  planar binary tree  permutation  weak order       font style='font-size:12px;'> 2015/8/14
Loday and Ronco defined an interesting Hopf algebra structure on the linear span of the set of planar binary trees. They showed that the inclusion of the Hopf algebra of non-commutative symmetric fu...
Matchings and phylogenetic trees     Matchings  system  the development tree       font style='font-size:12px;'> 2015/7/14
Matchings and phylogenetic trees
We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on 2n vert...
Pre-Lie algebras and the rooted trees operad     Pre-Lie algebras  rooted trees operad       font style='font-size:12px;'> 2015/3/25
A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatoria...
Disposition Polynomials and Plane Trees     disposition  disposition polynomial  plane tree  Prüfer correspondence       font style='font-size:12px;'> 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...

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