Related papers: Runs in Random Sequences over Ordered Sets
The distributions of the $m$-th longest runs of multivariate random sequences are considered. For random sequences made up of $k$ kinds of letters, the lengths of the runs are sorted in two ways to give two definitions of run length…
We introduce an algorithm for the uniform generation of infinite runs in concurrent systems under a partial order probabilistic semantics. We work with trace monoids as concurrency models. The algorithm outputs on-the-fly approximations of…
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…
The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…
From a mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. We consider distributions of runs and patterns related to run lengths of multi-state sequences,…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
We study the exact distributions of runs of a fixed length in variation which considers binary trials for which the probability of ones is geometrically varying. The random variable $E_{n,k}$ denote the number of success runs of a fixed…
Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
This article studies the dynamics of a finite chain with infinite components. The equation which permits us to find the probability distribution of the chain length is constructed and analysed. This research is a continuation of paper…
This note examines a problem in enumerative and asymptotic combinatorics involving the classical structure of integer compositions. What is sought is an analysis on average and in distribution of the length of the longest run of consecutive…
This note examines the question of randomness in a sequence based on the continued fraction (CF) representation of its corresponding representation as a number, or as D sequence. We propose a randomness measure that is directly equal to the…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
Let $V(k)$ denote the waiting time, the number of trials needed to get a consecutive $k$ ones. We propose recurrence algorithms for the probability distribution function (pdf) and the probability generating function (pgf) of $V(k)$ in…
We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting that have constant failure rate. In spite of the minimal algebraic structure, there is a…
Denote by {$\times$} the fractional part. We establish several new metrical results on the distribution properties of the sequence ({x n }) n$\ge$1. Many of them are presented in a more general framework, in which the sequence of functions…
In this paper we consider the density of maximal order elements in $\mathrm{GL}_n(q)$. Fixing any of the rank $n$ of the group, the characteristic $p$ or the degree $r$ of the extension of the underlying field $\mathbb{F}_q$ of size…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…