Related papers: Distributions of statistics on separable permutati…
Inversion sequences, also known as subexcedant sequences, form a fundamental class of objects in enumerative combinatorics. In this paper, we study the joint distribution of five statistics on inversion sequences. While several statistics…
Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…
An open conjecture in pattern avoidance theory is that the distribution of the major index among 321-avoiding permutations is distributed unimodally. We construct a formula for this distribution, and in the case of 2 descents prove…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…
We provide enumerative results concerning right-to-left minima and left- to-right minima in Andre' permutations of the first and second kind. For both the two kinds, the distribution of right-to-left and left-to-right minima is the same. We…
A permutation $\sigma$ of a multiset is called Stirling permutation if $\sigma(s)\ge \sigma(i)$ as soon as $\sigma(i)=\sigma(j)$ and $i<s<j.$ In our paper we study Stirling polynomials that arise in the generating function for descent…
We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…
A descent $k$ of a permutation $\pi=\pi_{1}\pi_{2}\dots\pi_{n}$ is called a big descent if $\pi_{k}>\pi_{k+1}+1$; denote the number of big descents of $\pi$ by $\operatorname{bdes}(\pi)$. We study the distribution of the…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
We introduce and study new refinements of inversion statistics for permutations, such as k-step inversions, (the number of inversions with fixed position differences) and non-inversion sums (the sum of the differences of positions of the…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
The development of the theories of the second-order Eulerian polynomials began with the works of Buckholtz and Carlitz in their studies of an asymptotic expansion. Gessel-Stanley introduced Stirling permutations and presented combinatorial…
We extend classical theorems of Renyi by finding the distributions of the numbers of both weak and strong left-to-right maxima (a.k.a. outstanding elements) in words over a given alphabet and in permutations of a given multiset.
We prove that the pair of statistics (des,maj) on multiset permutations is equidistributed with the pair (stc,inv) on certain quotients of the symmetric group. We define the analogue of the statistic stc on multiset permutations, whose…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We develop two novel approaches for constructing skewed and bimodal flexible distributions that can effectively generalize classical symmetric distributions. We illustrate the application of introduced techniques by extending normal,…
An $(X,Y)$-descent in a permutation is a pair of adjacent elements such that the first element is from $X$, the second element is from $Y$, and the first element is greater than the second one. An $(X,Y)$-adjacency in a permutation is a…
Permutation statistics $\wnm$ and $\rlm$ are both arising from permutation tableaux. $\wnm$ was introduced by Chen and Zhou, which was proved equally distributed with the number of unrestricted rows of a permutation tableau. While $\rlm$ is…
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…