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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
2023/11/15
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...
Groups of automorphisms of trees and their limit sets
Groups automorphisms trees limit sets
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...
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...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
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...
STRUCTURE OF THE LODAY-RONCO HOPF ALGEBRA OF TREES
Hopf algebra planar binary tree permutation weak order
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...
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...
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: Groups acting freely on Z^n-trees (Z^n-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to invest...
The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree
graph drawing planar graphs slopes planar slope number
2011/2/22
It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct ed...
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter. In the odd case, int...
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees
Sub-Gaussian tail conditioned Galton--Watson trees
2010/11/23
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we deriv...
Star graphs: threaded distance trees and E-sets
Star graphs threaded distance trees E-sets
2010/11/22
The distribution of distances in the star graph $ST_n$, ($1established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given...
We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures.
Completely Metrisable Groups Acting on Trees
Completely metrisable groups Locally compact groups Actions on trees
2010/12/15
We consider actions of completely metrisable groups on simplicial trees in the context of the Bass–Serre theory. Our main result characterises continuity of the amplitude function corresponding to a g...
Balanced binary trees in the Tamari lattice
balanced trees Tamari lattice posets grammars generating series combinatorics
2010/12/13
We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T0, T1] where T0 and T1 are balanced trees are isomorphic as posets to a hyp...