On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution

On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution

The influence of the iteration process on the structure of the graph Gπ of the uniform random substitution π : S → S is studied. Exact formulas are written out for the distribution of the length βπ (x) of the cycle Kπ (x) containing an arbitrary fixed vertex x ∈ S. An expression is written for the m...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Prikladnaya Diskretnaya Matematika 2023 (62), p.5-12
1. Verfasser: Mironkin, Vladimir O.
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 12
container_issue 62
container_start_page 5
container_title Prikladnaya Diskretnaya Matematika
container_volume
creator Mironkin, Vladimir O.
description The influence of the iteration process on the structure of the graph Gπ of the uniform random substitution π : S → S is studied. Exact formulas are written out for the distribution of the length βπ (x) of the cycle Kπ (x) containing an arbitrary fixed vertex x ∈ S. An expression is written for the mathematical expectation of a random variable λπk (l) equal to the number of vertices in the graph Gπk lying on cycles of length l ∈ {1, . . . , |S|}. For k ∈ N and arbitrary fixed vertices x, y ∈ S, x ̸= y, the joint probability of their falling on cycles of fixed lengths in the graph Gπk is calculated.
doi_str_mv 10.17223/20710410/62/1
format Article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_17223_20710410_62_1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_17223_20710410_62_1</sourcerecordid><originalsourceid>FETCH-crossref_primary_10_17223_20710410_62_13</originalsourceid><addsrcrecordid>eNqVj0FOwzAQRS0EEhXtlrUvkMYziRKxRiB2bNhbTuo0Ixw7mnEWvT1JoQdgNV9674_0lXoGc4QWsSrRtGBqMGWDJdypHVYABWJT3a95ZcUGH9VBhDpj6tbUDb7sVPiMOo9en0gyU7dkSlGnQfeXPngdfDznUTT9Smd287jR72JaQqZ5VSh7drfWJi2RhsSTZhdPadKydJIpXx_v1cPggvjD331Sx_e3r9ePouckwn6wM9Pk-GLB2Osse5tlG7RQ_bvwA9bdVTE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution</title><source>Math-Net.Ru (free access)</source><creator>Mironkin, Vladimir O.</creator><creatorcontrib>Mironkin, Vladimir O. ; MIREA - Russian Technological University</creatorcontrib><description>The influence of the iteration process on the structure of the graph Gπ of the uniform random substitution π : S → S is studied. Exact formulas are written out for the distribution of the length βπ (x) of the cycle Kπ (x) containing an arbitrary fixed vertex x ∈ S. An expression is written for the mathematical expectation of a random variable λπk (l) equal to the number of vertices in the graph Gπk lying on cycles of length l ∈ {1, . . . , |S|}. For k ∈ N and arbitrary fixed vertices x, y ∈ S, x ̸= y, the joint probability of their falling on cycles of fixed lengths in the graph Gπk is calculated.</description><identifier>ISSN: 2071-0410</identifier><identifier>EISSN: 2311-2263</identifier><identifier>DOI: 10.17223/20710410/62/1</identifier><language>eng</language><ispartof>Prikladnaya Diskretnaya Matematika, 2023 (62), p.5-12</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,4010,27900,27901,27902</link.rule.ids></links><search><creatorcontrib>Mironkin, Vladimir O.</creatorcontrib><creatorcontrib>MIREA - Russian Technological University</creatorcontrib><title>On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution</title><title>Prikladnaya Diskretnaya Matematika</title><description>The influence of the iteration process on the structure of the graph Gπ of the uniform random substitution π : S → S is studied. Exact formulas are written out for the distribution of the length βπ (x) of the cycle Kπ (x) containing an arbitrary fixed vertex x ∈ S. An expression is written for the mathematical expectation of a random variable λπk (l) equal to the number of vertices in the graph Gπk lying on cycles of length l ∈ {1, . . . , |S|}. For k ∈ N and arbitrary fixed vertices x, y ∈ S, x ̸= y, the joint probability of their falling on cycles of fixed lengths in the graph Gπk is calculated.</description><issn>2071-0410</issn><issn>2311-2263</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNqVj0FOwzAQRS0EEhXtlrUvkMYziRKxRiB2bNhbTuo0Ixw7mnEWvT1JoQdgNV9674_0lXoGc4QWsSrRtGBqMGWDJdypHVYABWJT3a95ZcUGH9VBhDpj6tbUDb7sVPiMOo9en0gyU7dkSlGnQfeXPngdfDznUTT9Smd287jR72JaQqZ5VSh7drfWJi2RhsSTZhdPadKydJIpXx_v1cPggvjD331Sx_e3r9ePouckwn6wM9Pk-GLB2Osse5tlG7RQ_bvwA9bdVTE</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Mironkin, Vladimir O.</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2023</creationdate><title>On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution</title><author>Mironkin, Vladimir O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-crossref_primary_10_17223_20710410_62_13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mironkin, Vladimir O.</creatorcontrib><creatorcontrib>MIREA - Russian Technological University</creatorcontrib><collection>CrossRef</collection><jtitle>Prikladnaya Diskretnaya Matematika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mironkin, Vladimir O.</au><aucorp>MIREA - Russian Technological University</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution</atitle><jtitle>Prikladnaya Diskretnaya Matematika</jtitle><date>2023</date><risdate>2023</risdate><issue>62</issue><spage>5</spage><epage>12</epage><pages>5-12</pages><issn>2071-0410</issn><eissn>2311-2263</eissn><abstract>The influence of the iteration process on the structure of the graph Gπ of the uniform random substitution π : S → S is studied. Exact formulas are written out for the distribution of the length βπ (x) of the cycle Kπ (x) containing an arbitrary fixed vertex x ∈ S. An expression is written for the mathematical expectation of a random variable λπk (l) equal to the number of vertices in the graph Gπk lying on cycles of length l ∈ {1, . . . , |S|}. For k ∈ N and arbitrary fixed vertices x, y ∈ S, x ̸= y, the joint probability of their falling on cycles of fixed lengths in the graph Gπk is calculated.</abstract><doi>10.17223/20710410/62/1</doi></addata></record>
fulltext fulltext
identifier ISSN: 2071-0410
ispartof Prikladnaya Diskretnaya Matematika, 2023 (62), p.5-12
issn 2071-0410
2311-2263
language eng
recordid cdi_crossref_primary_10_17223_20710410_62_1
source Math-Net.Ru (free access)
title On the distribution of cycle lengths in the graph of k-multiple iteration of the uniform random substitution
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-05T18%3A48%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20distribution%20of%20cycle%20lengths%20in%20the%20graph%20of%20k-multiple%20iteration%20of%20the%20uniform%20random%20substitution&rft.jtitle=Prikladnaya%20Diskretnaya%20Matematika&rft.au=Mironkin,%20Vladimir%20O.&rft.aucorp=MIREA%20-%20Russian%20Technological%20University&rft.date=2023&rft.issue=62&rft.spage=5&rft.epage=12&rft.pages=5-12&rft.issn=2071-0410&rft.eissn=2311-2263&rft_id=info:doi/10.17223/20710410/62/1&rft_dat=%3Ccrossref%3E10_17223_20710410_62_1%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true