Related papers: On some properties of permutation tableaux
We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the…
A brief presentation of basic definitions and notation used in permutation patterns research.
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The…
Given a permutation statistic $s : S_n \to \mathbb{R}$, define the mean statistic $\bar{s}$ as the statistic which computes the mean of $s$ over conjugacy classes. We describe a way to calculate the expected value of $s$ on a product of $t$…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
We construct bijections to show that two pairs of sextuple set-valued statistics of permutations are equidistributed on symmetric groups. This extends a recent result of Sokal and the second author valid for integer-valued statistics as…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding…
Inspired by the intimate relationship between Voiculescu's noncommutative probability theory (of type A) and large-N matrix models in physics, we look for physical models related to noncommutative probability theory of type B. These turn…
Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition…
This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from…
We study the random binary contingency tables with non-uniform margin. More precisely, for parameters $n,\delta,B,C$, we consider $X=(X_{ij})$ with $X_{ij}\in \lbrace 0,1\rbrace$, the random binary contingency tables whose first…
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…