Base Partition for Mixed Families of Finitary and Cofinitary Matroids
Let be a finite or infinite family consisting of matroids on a common ground set E each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each M i , which covers the set E , and also a collection of bases which are...
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| Veröffentlicht in: | Combinatorica (Budapest. 1981) 2021-02, Vol.41 (1), p.31-52 |
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| container_title | Combinatorica (Budapest. 1981) |
| container_volume | 41 |
| creator | Erde, Joshua Gollin, J. Pascal Joó, Attila Knappe, Paul Pitz, Max |
| description | Let
be a finite or infinite family consisting of matroids on a common ground set
E
each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each
M
i
, which covers the set
E
, and also a collection of bases which are pairwise disjoint, then there is a collection of bases which partition
E.
We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC. |
| doi_str_mv | 10.1007/s00493-020-4422-4 |
| format | Article |
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be a finite or infinite family consisting of matroids on a common ground set
E
each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each
M
i
, which covers the set
E
, and also a collection of bases which are pairwise disjoint, then there is a collection of bases which partition
E.
We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC.</description><identifier>ISSN: 0209-9683</identifier><identifier>EISSN: 1439-6912</identifier><identifier>DOI: 10.1007/s00493-020-4422-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Axioms ; Collection ; Combinatorics ; Family ; Mathematics ; Mathematics and Statistics ; Matrix partitioning ; Original Paper ; Set theory</subject><ispartof>Combinatorica (Budapest. 1981), 2021-02, Vol.41 (1), p.31-52</ispartof><rights>János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2021</rights><rights>COPYRIGHT 2021 Springer</rights><rights>János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-7d066a435573c20d3eb01cff9646666090967357b6bbe4fc567db3ba1c8ad3ce3</citedby><cites>FETCH-LOGICAL-c355t-7d066a435573c20d3eb01cff9646666090967357b6bbe4fc567db3ba1c8ad3ce3</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/s00493-020-4422-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00493-020-4422-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Erde, Joshua</creatorcontrib><creatorcontrib>Gollin, J. Pascal</creatorcontrib><creatorcontrib>Joó, Attila</creatorcontrib><creatorcontrib>Knappe, Paul</creatorcontrib><creatorcontrib>Pitz, Max</creatorcontrib><title>Base Partition for Mixed Families of Finitary and Cofinitary Matroids</title><title>Combinatorica (Budapest. 1981)</title><addtitle>Combinatorica</addtitle><description>Let
be a finite or infinite family consisting of matroids on a common ground set
E
each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each
M
i
, which covers the set
E
, and also a collection of bases which are pairwise disjoint, then there is a collection of bases which partition
E.
We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC.</description><subject>Axioms</subject><subject>Collection</subject><subject>Combinatorics</subject><subject>Family</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix partitioning</subject><subject>Original Paper</subject><subject>Set theory</subject><issn>0209-9683</issn><issn>1439-6912</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kE1PAyEQhonRxFr9Ad428UwdPpZdjrVp1USjBz0Tlo-Gpl0qbBP999KsxpNwYJh53xl4ELomMCMAzW0G4JJhoIA5pxTzEzQhnEksJKGnaFIKEkvRsnN0kfMGAFpG6gla3unsqledhjCE2Fc-puo5fDpbrfQubIPLVfTVKvRh0Omr0r2tFtH_Xp_1kGKw-RKdeb3N7urnnKL31fJt8YCfXu4fF_MnbFhdD7ixIITmJW6YoWCZ64AY76XgoiyQIEXD6qYTXee4N7VobMc6TUyrLTOOTdHN2Hef4sfB5UFt4iH1ZaSiNfCWyZrKopqNqrXeOhV6H4ekTdnW7YKJvfOh5OcNkUBbWUBMERkNJsWck_Nqn8KufFARUEe8asSrCkV1xKt48dDRk4u2X7v095T_Td80_Xt6</recordid><startdate>20210201</startdate><enddate>20210201</enddate><creator>Erde, Joshua</creator><creator>Gollin, J. Pascal</creator><creator>Joó, Attila</creator><creator>Knappe, Paul</creator><creator>Pitz, Max</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210201</creationdate><title>Base Partition for Mixed Families of Finitary and Cofinitary Matroids</title><author>Erde, Joshua ; Gollin, J. Pascal ; Joó, Attila ; Knappe, Paul ; Pitz, Max</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-7d066a435573c20d3eb01cff9646666090967357b6bbe4fc567db3ba1c8ad3ce3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Axioms</topic><topic>Collection</topic><topic>Combinatorics</topic><topic>Family</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix partitioning</topic><topic>Original Paper</topic><topic>Set theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Erde, Joshua</creatorcontrib><creatorcontrib>Gollin, J. Pascal</creatorcontrib><creatorcontrib>Joó, Attila</creatorcontrib><creatorcontrib>Knappe, Paul</creatorcontrib><creatorcontrib>Pitz, Max</creatorcontrib><collection>CrossRef</collection><jtitle>Combinatorica (Budapest. 1981)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Erde, Joshua</au><au>Gollin, J. Pascal</au><au>Joó, Attila</au><au>Knappe, Paul</au><au>Pitz, Max</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Base Partition for Mixed Families of Finitary and Cofinitary Matroids</atitle><jtitle>Combinatorica (Budapest. 1981)</jtitle><stitle>Combinatorica</stitle><date>2021-02-01</date><risdate>2021</risdate><volume>41</volume><issue>1</issue><spage>31</spage><epage>52</epage><pages>31-52</pages><issn>0209-9683</issn><eissn>1439-6912</eissn><abstract>Let
be a finite or infinite family consisting of matroids on a common ground set
E
each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each
M
i
, which covers the set
E
, and also a collection of bases which are pairwise disjoint, then there is a collection of bases which partition
E.
We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00493-020-4422-4</doi><tpages>22</tpages></addata></record> |
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| ispartof | Combinatorica (Budapest. 1981), 2021-02, Vol.41 (1), p.31-52 |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Axioms Collection Combinatorics Family Mathematics Mathematics and Statistics Matrix partitioning Original Paper Set theory |
| title | Base Partition for Mixed Families of Finitary and Cofinitary Matroids |
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