On cogrowth function of algebras and its logarithmical gap

On cogrowth function of algebras and its logarithmical gap

Let \(A \cong k\langle X \rangle / I\) be an associative algebra. A finite word over alphabet \(X\) is \(I\){\it-reducible} if its image in \(A\) is a \(k\)-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal \(I\)-reducible word. A {\em cogrowth} f...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2020-01
Hauptverfasser: Kanel-Belov, A J, Melnikov, I A, Mitrofanov, I V
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics - Combinatorics
Mathematics - Rings and Algebras
Obstructions
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Kanel-Belov, A J
Melnikov, I A
Mitrofanov, I V
description Let \(A \cong k\langle X \rangle / I\) be an associative algebra. A finite word over alphabet \(X\) is \(I\){\it-reducible} if its image in \(A\) is a \(k\)-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal \(I\)-reducible word. A {\em cogrowth} function is number of obstructions of length \(\le n\). We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.
doi_str_mv 10.48550/arxiv.1912.03345
format Article
fullrecord <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1912_03345</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2323278122</sourcerecordid><originalsourceid>FETCH-LOGICAL-a522-ac9214fea91efd39d3d76fcd835834edd3c3d3cd7a6fb9df0480c4b249fc7ead3</originalsourceid><addsrcrecordid>eNotj01Lw0AYhBdBsNT-AE8ueE7cfd_dJvEmRa1Q6KX38HY_0pQ0GzeJH__e2MowzGUY5mHsTopU5VqLR4rf9WcqCwmpQFT6is0AUSa5Arhhi74_CiFgmYHWOGNP25abUMXwNRy4H1sz1KHlwXNqKreP1HNqLa-HnjeholgPh1NtqOEVdbfs2lPTu8V_ztnu9WW3Wieb7dv76nmTkAZIyBQglXdUSOctFhZttvTG5qhzVM5aNDjZZrT0-8J6oXJh1B5U4U3myOKc3V9mz2BlF-sTxZ_yD7A8A06Nh0uji-FjdP1QHsMY2-lTCTgpyyUA_gIl3FPf</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2323278122</pqid></control><display><type>article</type><title>On cogrowth function of algebras and its logarithmical gap</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Kanel-Belov, A J ; Melnikov, I A ; Mitrofanov, I V</creator><creatorcontrib>Kanel-Belov, A J ; Melnikov, I A ; Mitrofanov, I V</creatorcontrib><description>Let \(A \cong k\langle X \rangle / I\) be an associative algebra. A finite word over alphabet \(X\) is \(I\){\it-reducible} if its image in \(A\) is a \(k\)-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal \(I\)-reducible word. A {\em cogrowth} function is number of obstructions of length \(\le n\). We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1912.03345</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Mathematics - Combinatorics ; Mathematics - Rings and Algebras ; Obstructions</subject><ispartof>arXiv.org, 2020-01</ispartof><rights>2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27902</link.rule.ids><backlink>$$Uhttps://doi.org/10.5802/crmath.170$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.1912.03345$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kanel-Belov, A J</creatorcontrib><creatorcontrib>Melnikov, I A</creatorcontrib><creatorcontrib>Mitrofanov, I V</creatorcontrib><title>On cogrowth function of algebras and its logarithmical gap</title><title>arXiv.org</title><description>Let \(A \cong k\langle X \rangle / I\) be an associative algebra. A finite word over alphabet \(X\) is \(I\){\it-reducible} if its image in \(A\) is a \(k\)-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal \(I\)-reducible word. A {\em cogrowth} function is number of obstructions of length \(\le n\). We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.</description><subject>Algebra</subject><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Rings and Algebras</subject><subject>Obstructions</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><sourceid>GOX</sourceid><recordid>eNotj01Lw0AYhBdBsNT-AE8ueE7cfd_dJvEmRa1Q6KX38HY_0pQ0GzeJH__e2MowzGUY5mHsTopU5VqLR4rf9WcqCwmpQFT6is0AUSa5Arhhi74_CiFgmYHWOGNP25abUMXwNRy4H1sz1KHlwXNqKreP1HNqLa-HnjeholgPh1NtqOEVdbfs2lPTu8V_ztnu9WW3Wieb7dv76nmTkAZIyBQglXdUSOctFhZttvTG5qhzVM5aNDjZZrT0-8J6oXJh1B5U4U3myOKc3V9mz2BlF-sTxZ_yD7A8A06Nh0uji-FjdP1QHsMY2-lTCTgpyyUA_gIl3FPf</recordid><startdate>20200113</startdate><enddate>20200113</enddate><creator>Kanel-Belov, A J</creator><creator>Melnikov, I A</creator><creator>Mitrofanov, I V</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20200113</creationdate><title>On cogrowth function of algebras and its logarithmical gap</title><author>Kanel-Belov, A J ; Melnikov, I A ; Mitrofanov, I V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a522-ac9214fea91efd39d3d76fcd835834edd3c3d3cd7a6fb9df0480c4b249fc7ead3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algebra</topic><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Rings and Algebras</topic><topic>Obstructions</topic><toplevel>online_resources</toplevel><creatorcontrib>Kanel-Belov, A J</creatorcontrib><creatorcontrib>Melnikov, I A</creatorcontrib><creatorcontrib>Mitrofanov, I V</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kanel-Belov, A J</au><au>Melnikov, I A</au><au>Mitrofanov, I V</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On cogrowth function of algebras and its logarithmical gap</atitle><jtitle>arXiv.org</jtitle><date>2020-01-13</date><risdate>2020</risdate><eissn>2331-8422</eissn><abstract>Let \(A \cong k\langle X \rangle / I\) be an associative algebra. A finite word over alphabet \(X\) is \(I\){\it-reducible} if its image in \(A\) is a \(k\)-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal \(I\)-reducible word. A {\em cogrowth} function is number of obstructions of length \(\le n\). We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1912.03345</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2020-01
issn 2331-8422
language eng
recordid cdi_arxiv_primary_1912_03345
source arXiv.org; Free E- Journals
subjects Algebra
Mathematics - Combinatorics
Mathematics - Rings and Algebras
Obstructions
title On cogrowth function of algebras and its logarithmical gap
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-05T19%3A07%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20cogrowth%20function%20of%20algebras%20and%20its%20logarithmical%20gap&rft.jtitle=arXiv.org&rft.au=Kanel-Belov,%20A%20J&rft.date=2020-01-13&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1912.03345&rft_dat=%3Cproquest_arxiv%3E2323278122%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2323278122&rft_id=info:pmid/&rfr_iscdi=true