Related papers: Mixed succession rules: the commutative case
Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.
A pedigree is a directed graph in which each vertex (except the founder vertices) has two parents. The main result in this paper is a construction of an infinite family of counter examples to a reconstruction problem on pedigrees, thus…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…
We present a pumping lemma for each level of the collapsible pushdown graph hierarchy in analogy to the second author's pumping lemma for higher-order pushdown graphs (without collapse). Using this lemma, we give the first known examples…
We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order…
Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
Three-graded root systems can be arranged into nested sequences. One exceptional sequence provides a natural means to recover some structures and symmetries familiar in the context of particle physics.
We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
Deep generative models have been shown powerful in generating novel molecules with desired chemical properties via their representations such as strings, trees or graphs. However, these models are limited in recommending synthetic routes…
In this paper we introduce mixed coloured permutation, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the generating function, closed forms, recursions and…
We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
In this paper, we first propose a new extended mixture model of residual lifetime distributions. We show that this model is suitable in modeling residual lifetime in some practical situations. Several closure properties of some well-known…
Our goal in this paper is to automatically extract a set of decision rules (rule set) that best explains a classification data set. First, a large set of decision rules is extracted from a set of decision trees trained on the data set. The…
Here, we present a family of time series with a simple growth constraint. This family can be the basis of a model to apply to emerging computation in business and micro-economy where global functions can be expressed from local rules. We…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…