Related papers: Statistics on Wreath Products and Generalized Bino…
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…
We introduce multinomial and $r$-variants of several classic objects of combinatorial probability, such as the random recursive and Hoppe trees, random set partitions and compositions, the Chinese restaurant process, Feller's coupling, and…
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…
In this paper we introduce mixed coloured permutation, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the generating function, closed forms, recursions and…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
We present a full description of the Bieri-Neumann-Strebel invariant of restricted permutational wreath products of groups. We also give partial results about the 2-dimensional homotopical invariant of such groups. These results may be…
We prove a conjecture of Haglund which can be seen as an extension of the equidistribution of the inversion number and the major index over permutations to ordered set partitions. Haglund's conjecture implicitly defines two statistics on…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an…
A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the…
A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X \wr Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
The distribution of certain Mahonian statistic (called $\mathrm{BAST}$) introduced by Babson and Steingr\'{i}msson over the set of permutations that avoid vincular pattern $1\underline{32}$, is shown bijectively to match the distribution of…
We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
A random number of items each independently marked with one of a collection of colours gives rise to the multinomial marking, which generalises binomial thinning. A multivariate version, where previously marked items are then re-marked, has…
We develop a new algebraic framework to reason about languages of Mazurkiewicz traces. This framework supports true concurrency and provides a non-trivial generalization of the wreath product operation to the trace setting. A novel local…