{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T02:48:47Z","timestamp":1785293327547,"version":"3.55.0"},"reference-count":22,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"4","license":[{"start":{"date-parts":[[2011,4,1]],"date-time":"2011-04-01T00:00:00Z","timestamp":1301616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2011,4]]},"DOI":"10.1109\/tit.2011.2111890","type":"journal-article","created":{"date-parts":[[2011,3,15]],"date-time":"2011-03-15T17:08:26Z","timestamp":1300208906000},"page":"1849-1864","source":"Crossref","is-referenced-by-count":9,"title":["The Minimal Set of Ingleton Inequalities"],"prefix":"10.1109","volume":"57","author":[{"given":"L","family":"Guille","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T","family":"Chan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Grant","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928963"},{"key":"ref11","author":"chan","year":"1998","journal-title":"Aspects of Information Inequalities and Its Applications"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.1013138"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/18.681320"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1677"},{"key":"ref15","first-page":"149","article-title":"Common information is far less than mutual information","volume":"2","author":"gacs","year":"1973","journal-title":"Probl Control Inf Theory"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/18.641556"},{"key":"ref17","author":"schrijver","year":"2003","journal-title":"Combinatorial Optimization Polyhedra and Efficiency (Algorithms and Combinatorics)"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/18.850663"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.807285"},{"key":"ref4","first-page":"185","article-title":"Probabilistic conditional independence structures and matroid theory: Background","author":"mat","year":"1994","journal-title":"Int J Gen Syst"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8608-5","author":"yeung","year":"2002","journal-title":"A First Course in Information Theory"},{"key":"ref6","article-title":"Linear rank inequalities on five or more variables","author":"dougherty","year":"2009","journal-title":"arXiv cs IT\/0910 0284v3"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2009.10.014"},{"key":"ref8","first-page":"41","article-title":"Infinitely many information inequalities","author":"mat","year":"2007","journal-title":"Proc 2007 IEEE Int Symp Information Theory"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2010.5513542"},{"key":"ref2","first-page":"149","article-title":"Representation of matroids","author":"ingleton","year":"1971","journal-title":"Combin Math Appl"},{"key":"ref1","author":"oxley","year":"1992","journal-title":"Matroid Theory"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1561\/0100000007I"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.851744"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2010.5513732"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.820015"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/18\/5730547\/05730560.pdf?arnumber=5730560","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,10]],"date-time":"2021-10-10T23:52:33Z","timestamp":1633909953000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/5730560\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4]]},"references-count":22,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1109\/tit.2011.2111890","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,4]]}}}