Related papers: Statistics on bargraphs of inversion sequences of …
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.
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
Given a permutation statistic $\operatorname{st}$, define its inverse statistic $\operatorname{ist}$ by $\operatorname{ist}(\pi):=\operatorname{st}(\pi^{-1})$. We give a general approach, based on the theory of symmetric functions, for…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…
We prove two estimates for the expectation of the exponential of a complex function of a random permutation or subset. Using this theory, we find asymptotic expressions for the expected number of copies and induced copies of a given graph…
In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
For a given permutation $\pi_n$ in $S_n$, a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (\pi_n(i) - \pi_n (j)) < 0$. In this paper, we study various statistics of random…
We derive a generating function for the number of integer compositions of $n$ into $k$ parts (i.e., $k$-compositions of $n$) with a given number of inversions, and obtain similar results for $k$-compositions of $n$ with a given number of…
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
A ballot permutation is a permutation $\pi$ such that in any prefix of $\pi$ the descent number is not more than the ascent number. By using a reversal concatenation map, we give a formula for the joint distribution (pk, des) of the peak…
Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al. found distributions of ascents and descents on permutations avoiding any…
We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide…
Two well-known distributions in the study of permutation statistics are the Mahonian and Eulerian distributions. Mahonian statistics include the major index MAJ and the number of inversions INV, while examples of Eulerian statistics are the…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…