Related papers: An involution on bicubic maps and \beta(0,1)-trees
It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…
We consider the problem of enumerating d-irreducible maps, i.e. planar maps whose all cycles have length at least d, and such that any cycle of length d is the boundary of a face of degree d. We develop two approaches in parallel: the…
We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of…
We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…
Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series $\psi(x, y, z; 1, 1+\beta)$ with an additional parameter $\beta$ that may be interpreted as a continuous deformation of the rooted…
Matrix transposition induces an involution on the isomorphism classes of semi-simple n-dimensional representations of the three string braid group. We show that a connected component of this variety can detect braid-reversion or that the…
We present bijections enumerating (k,m)-trees, k-gon trees, edge labelled (2,1)-trees, and other tree-like structures. Our constructions are based on Foata's (1971) bijection for cycle-free functions, which is simplified here.
Let $T(n,m)$ be the set of all plane labelled bipartite trees with $n$ white vertices and $m$ black. If the number $n+m$ of vertices is even, then the set $T(n,m)$ is a union of two disjoint subsets --- subset od "even" trees and subset of…
This paper extends those of Glendinning and Sidorov [3] and of Hare and Sidorov [6] from the case of the doubling map to the more general $\beta$-transformation. Let $\beta \in (1,2)$ and consider the $\beta$-transformation…
The Pathwidth Theorem states that if a class of graphs has unbounded pathwidth, then it contains all trees as graph minors. We prove a similar result for dense graphs. More precisely, we give a finite family of tree-like patterns and prove…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…
The Tree Decomposition Conjecture by Bar\'at and Thomassen states that for every tree $T$ there exists a natural number $k(T)$ such that the following holds: If $G$ is a $k(T)$-edge-connected simple graph with size divisible by the size of…
We study the fixed point theory of n-valued maps of a space X using the fixed point theory of maps between X and its configuration spaces. We give some general results to decide whether an n-valued map can be deformed to a fixed point free…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
Seo and Shin showed that the number of rooted trees on $[n+1]$ such that the maximal decreasing subtree with the same root has $k+1$ vertices is equal to the number of functions $f:[n]\to[n]$ such that the image of $f$ contains $[k]$. We…
The decomposition of a density function on a domain into a minimal sum of unimodal components is a fundamental problem in statistics, leading to the topological invariant of unimodal category of a density. This paper gives an efficient…
This study examines the tree models of mildly dissipative diffeomorphisms on the disk $\D$. These models are one-dimensional dynamical systems with ergodic aperiodic data as well as some properties of the original dynamics. The focus of…