图中k次迭代的一致随机映射的顶点和分量的碰撞和关联

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-08-01 DOI:10.1515/dma-2021-0023

V. O. Mironkin

{"title":"图中k次迭代的一致随机映射的顶点和分量的碰撞和关联","authors":"V. O. Mironkin","doi":"10.1515/dma-2021-0023","DOIUrl":null,"url":null,"abstract":"Abstract The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"259 - 269"},"PeriodicalIF":0.3000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping\",\"authors\":\"V. O. Mironkin\",\"doi\":\"10.1515/dma-2021-0023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.\",\"PeriodicalId\":11287,\"journal\":{\"name\":\"Discrete Mathematics and Applications\",\"volume\":\"31 1\",\"pages\":\"259 - 269\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/dma-2021-0023\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2021-0023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

摘要研究了均匀随机映射的k次迭代图的概率特征。在一定的限制条件下，计算了任意顶点的非周期段长度的分布公式。我们得到了两个任意顶点属于同一连通分量的概率、任意顶点属于另一个顶点的原像集的概率以及图中存在碰撞的概率的精确表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping

Abstract The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.