Classes of Matroids Closed Under Minors and Principal Extensions

Classes of Matroids Closed Under Minors and Principal Extensions

This work studies the classes of matroids that are closed under minors, addition of coloops and principal extensions. To any matroid M in such a class a matroid M ° is constructed such that it contains M as a minor, has all proper minors in the class and violates Zhang- Yeung inequality. When the cl...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Combinatorica (Budapest. 1981) 2018-08, Vol.38 (4), p.935-954
1. Verfasser: Matus, Frantisek
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Inequality
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 954
container_issue 4
container_start_page 935
container_title Combinatorica (Budapest. 1981)
container_volume 38
creator Matus, Frantisek
description This work studies the classes of matroids that are closed under minors, addition of coloops and principal extensions. To any matroid M in such a class a matroid M ° is constructed such that it contains M as a minor, has all proper minors in the class and violates Zhang- Yeung inequality. When the class enjoys the inequality the matroid M ° becomes an excluded minor. An analogous assertion was known before for the linear matroids over any infinite field in connection with Ingleton inequality. The result is applied to the classes of multilinear, algebraic and almost entropic matroids. In particular, the class of almost entropic matroids has infinitely many excluded minors.
doi_str_mv 10.1007/s00493-017-3534-y
format Article
fullrecord <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2097639158</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A729115156</galeid><sourcerecordid>A729115156</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-54118fc82d92723db1277d2ffbb0f3296fcd692b5dbef760373711e9f8cf6ae23</originalsourceid><addsrcrecordid>eNp1kMtKAzEUhoMoWKsP4G7A9dScZDKZ7CylXqBFF3YdMpOkpEyTmkzBvr0pI7iSLA6E_zuXD6F7wDPAmD8mjCtBSwy8pIxW5ekCTaCioqwFkEs0wQSLUtQNvUY3Ke0wxg0FNkFPi16lZFIRbLFWQwxOp2LRh2R0sfHaxGLtfIipUF4XH9H5zh1UXyy_B-OTCz7doiur-mTufusUbZ6Xn4vXcvX-8raYr8qOMjaUrAJobNcQLQgnVLdAONfE2rbFlhJR207XgrRMt8byGlNOOYARtulsrQyhU_Qw9j3E8HU0aZC7cIw-j5T5NF5TAazJqdmY2qreSOdtGKLq8tNm77rgjXX5f86JAGDA6gzACHQxpBSNlYfo9iqeJGB5NitHszKblWez8pQZMjIpZ_3WxL9V_od-AF53eu0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2097639158</pqid></control><display><type>article</type><title>Classes of Matroids Closed Under Minors and Principal Extensions</title><source>Springer Nature - Complete Springer Journals</source><creator>Matus, Frantisek</creator><creatorcontrib>Matus, Frantisek</creatorcontrib><description>This work studies the classes of matroids that are closed under minors, addition of coloops and principal extensions. To any matroid M in such a class a matroid M ° is constructed such that it contains M as a minor, has all proper minors in the class and violates Zhang- Yeung inequality. When the class enjoys the inequality the matroid M ° becomes an excluded minor. An analogous assertion was known before for the linear matroids over any infinite field in connection with Ingleton inequality. The result is applied to the classes of multilinear, algebraic and almost entropic matroids. In particular, the class of almost entropic matroids has infinitely many excluded minors.</description><identifier>ISSN: 0209-9683</identifier><identifier>EISSN: 1439-6912</identifier><identifier>DOI: 10.1007/s00493-017-3534-y</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Combinatorics ; Inequality ; Mathematics ; Mathematics and Statistics</subject><ispartof>Combinatorica (Budapest. 1981), 2018-08, Vol.38 (4), p.935-954</ispartof><rights>János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Copyright Springer Science &amp; Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-54118fc82d92723db1277d2ffbb0f3296fcd692b5dbef760373711e9f8cf6ae23</citedby><cites>FETCH-LOGICAL-c355t-54118fc82d92723db1277d2ffbb0f3296fcd692b5dbef760373711e9f8cf6ae23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00493-017-3534-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00493-017-3534-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Matus, Frantisek</creatorcontrib><title>Classes of Matroids Closed Under Minors and Principal Extensions</title><title>Combinatorica (Budapest. 1981)</title><addtitle>Combinatorica</addtitle><description>This work studies the classes of matroids that are closed under minors, addition of coloops and principal extensions. To any matroid M in such a class a matroid M ° is constructed such that it contains M as a minor, has all proper minors in the class and violates Zhang- Yeung inequality. When the class enjoys the inequality the matroid M ° becomes an excluded minor. An analogous assertion was known before for the linear matroids over any infinite field in connection with Ingleton inequality. The result is applied to the classes of multilinear, algebraic and almost entropic matroids. In particular, the class of almost entropic matroids has infinitely many excluded minors.</description><subject>Combinatorics</subject><subject>Inequality</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0209-9683</issn><issn>1439-6912</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kMtKAzEUhoMoWKsP4G7A9dScZDKZ7CylXqBFF3YdMpOkpEyTmkzBvr0pI7iSLA6E_zuXD6F7wDPAmD8mjCtBSwy8pIxW5ekCTaCioqwFkEs0wQSLUtQNvUY3Ke0wxg0FNkFPi16lZFIRbLFWQwxOp2LRh2R0sfHaxGLtfIipUF4XH9H5zh1UXyy_B-OTCz7doiur-mTufusUbZ6Xn4vXcvX-8raYr8qOMjaUrAJobNcQLQgnVLdAONfE2rbFlhJR207XgrRMt8byGlNOOYARtulsrQyhU_Qw9j3E8HU0aZC7cIw-j5T5NF5TAazJqdmY2qreSOdtGKLq8tNm77rgjXX5f86JAGDA6gzACHQxpBSNlYfo9iqeJGB5NitHszKblWez8pQZMjIpZ_3WxL9V_od-AF53eu0</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Matus, Frantisek</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180801</creationdate><title>Classes of Matroids Closed Under Minors and Principal Extensions</title><author>Matus, Frantisek</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-54118fc82d92723db1277d2ffbb0f3296fcd692b5dbef760373711e9f8cf6ae23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Combinatorics</topic><topic>Inequality</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Matus, Frantisek</creatorcontrib><collection>CrossRef</collection><jtitle>Combinatorica (Budapest. 1981)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Matus, Frantisek</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Classes of Matroids Closed Under Minors and Principal Extensions</atitle><jtitle>Combinatorica (Budapest. 1981)</jtitle><stitle>Combinatorica</stitle><date>2018-08-01</date><risdate>2018</risdate><volume>38</volume><issue>4</issue><spage>935</spage><epage>954</epage><pages>935-954</pages><issn>0209-9683</issn><eissn>1439-6912</eissn><abstract>This work studies the classes of matroids that are closed under minors, addition of coloops and principal extensions. To any matroid M in such a class a matroid M ° is constructed such that it contains M as a minor, has all proper minors in the class and violates Zhang- Yeung inequality. When the class enjoys the inequality the matroid M ° becomes an excluded minor. An analogous assertion was known before for the linear matroids over any infinite field in connection with Ingleton inequality. The result is applied to the classes of multilinear, algebraic and almost entropic matroids. In particular, the class of almost entropic matroids has infinitely many excluded minors.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00493-017-3534-y</doi><tpages>20</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0209-9683
ispartof Combinatorica (Budapest. 1981), 2018-08, Vol.38 (4), p.935-954
issn 0209-9683
1439-6912
language eng
recordid cdi_proquest_journals_2097639158
source Springer Nature - Complete Springer Journals
subjects Combinatorics
Inequality
Mathematics
Mathematics and Statistics
title Classes of Matroids Closed Under Minors and Principal Extensions
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T13%3A19%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Classes%20of%20Matroids%20Closed%20Under%20Minors%20and%20Principal%20Extensions&rft.jtitle=Combinatorica%20(Budapest.%201981)&rft.au=Matus,%20Frantisek&rft.date=2018-08-01&rft.volume=38&rft.issue=4&rft.spage=935&rft.epage=954&rft.pages=935-954&rft.issn=0209-9683&rft.eissn=1439-6912&rft_id=info:doi/10.1007/s00493-017-3534-y&rft_dat=%3Cgale_proqu%3EA729115156%3C/gale_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2097639158&rft_id=info:pmid/&rft_galeid=A729115156&rfr_iscdi=true