Related papers: Mixed succession rules: the commutative case
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
We introduce weighted succession rules and parametric production matrices - simple extensions of the standard ECO method succession rules and production matrices. The purpose is to enumerate combinatorial objects with respect to several…
We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in…
We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of a production matrix. This allows us to combine our method with other enumeration techniques using matrices, such as the method…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous…
In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Given a gene tree and a species tree, ancestral configurations represent the combinatorially distinct sets of gene lineages that can reach a given node of the species tree. They have been introduced as a data structure for use in the…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
We study combinatorial structures arising from finite-time transition probabilities of the Totally Asymmetric Simple Exclusion Process with open boundary conditions. While much of the existing combinatorial theory regarding the TASEP…
Phylogenetic mixture models, in which the sites in sequences undergo different substitution processes along the same or different trees, allow the description of heterogeneous evolutionary processes. As data sets consisting of longer…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
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,…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…