Related papers: Smirnov Trees
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
This paper investigates two involutions on binary trees. One is the mirror symmetry of binary trees which combined with the classical bijection $\varphi$ between binary trees and plane trees answers an open problem posed by Bai and Chen.…
As a unification of increasing trees and plane trees, the weakly increasing trees labeled by a multiset was introduced by Lin-Ma-Ma-Zhou in 2021. Motived by some symmetries in plane trees proved recently by Dong, Du, Ji and Zhang, we…
The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
This article presents two novel algorithms for generating random increasing trees. The first algorithm efficiently generates strictly increasing binary trees using an ad hoc method. The second algorithm improves the recursive method for…
We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yield a new formula for the number of NATs. We also obtain…
We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition…
An m-extracting procedure produces unbiased random bits from a loaded dice with m faces. A binarization takes inputs from an m-faced dice and produce bit sequences to be fed into a (binary) extracting procedure to obtain random bits. Thus,…
We introduce and study a new notion of patterns in Stirling and $k$-Stirling permutations, which we call block patterns. We prove a general result which allows us to compute generating functions for the occurrences of various block patterns…
Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for…
A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
We introduce weighted regular tree grammars with storage as combination of (a) regular tree grammars with storage and (b) weighted tree automata over multioperator monoids. Each weighted regular tree grammar with storage generates a…
We prove a dualization of the Graham--Rothschild Theorem for variable words indexed by homogeneous trees.
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.