Related papers: Crossing and alignments of permutations

The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain…

We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…

Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation…

We consider the partially asymmetric simple exclusion process (PASEP) when its steady-state probability distribution function can be written in terms of a linear superposition of product measures with a finite number of shocks. In this case…

A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is…

We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…

We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…

Complex interactions between genes or proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded method for the cross-species analysis of interaction networks by {\em alignment}, which maps…

We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP.…

We give some results about a bijection associating each permutation with a subexcedant function. This function is related to a particular decomposition of the permutation as a product of transpositions and therefore it has been called…

We consider a partially asymmetric exclusion process (PASEP) on a finite number of sites with open and directed boundary conditions. Its partition function was calculated by Blythe, Evans, Colaiori, and Essler. It is known to be a…

We examine the enumeration of certain Motzkin objects according to the numbers of crossings and nestings. With respect to continued fractions, we compute and express the distributions of the statistics of the numbers of crossings and…

The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of N sites. It is partially asymmetric…

In this paper, we compute the distributions of the statistic number of crossings over permutations avoiding one of the pairs $\{321,231\}$, $\{123,132\}$ and $\{123,213\}$. The obtained results are new combinatorial interpretations of two…

Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of crossings. For each family, we express the generating function…

In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…

Nonnesting permutations are permutations of the multiset $\{1,1,2,2,\dots,n,n\}$ that avoid subsequences of the form $abba$ for any $a\neq b$. These permutations have recently been studied in connection to noncrossing (also called…

We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…

In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…

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…