Related papers: Patterns in Permutations and Involutions: A Struct…
We describe some configurations of conjugate permutations which may be used as a mathematical model of some genetical processes and crystal growth.
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models.…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.
In this working paper, we present a simple theoretical framework based on network theory to study how speciation, the process by which new species appear, shapes spatial patterns of diversity. We show that this framework can be expanded to…
Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecomposable permutations were studied in the literature in various…
In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$,…
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
Different ways to describe a permutation, as a sequence of integers, or a product of Coxeter generators, or a tree, give different choices to define a simple permutation. We recollect few of them, define new types of simple permutations,…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Enumerative geometry, the art and science of counting geometric objects satisfying geometric conditions, has seen a resurgence of activity in recent years due to an influx of new techniques that allow for enriched computations. This paper…