Runs in random sequences over ordered sets

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-08-13 DOI:10.1016/j.dam.2025.07.037

Tanner Reese

引用次数: 0

Abstract

We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance, and probability generating function (PGF) of such lengths in the case of an arbitrary total order. Our focus is on the case of distributions with both atoms and diffuse (absolutely or singularly continuous) mass which has not been addressed in this generality before. We also provide a method of calculating the PGF of run lengths for countably series–parallel partial orders. Additionally, we prove a strong law of large numbers for the distribution of run lengths in a particular realization of an infinite sequence.

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在有序集合上以随机序列运行

我们确定了全序集（全序）或偏序集（偏序）中元素的随机序列的运行长度分布。特别是，在任意总阶的情况下，我们为期望值、方差和概率生成函数（PGF）产生了新的公式。我们的重点是原子和扩散（绝对或奇异连续）质量的分布，这在以前的一般情况下没有得到解决。我们还提供了一种计算可数串并联偏序运行长度的PGF的方法。此外，我们还证明了在无限数列的特定实现中，行程长度分布的一个强大数定律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.