{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813297,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A Sunflower is a subset $S$ of a lattice, with the property that the meet of any two elements in $S$ coincides with the meet of all of $S$. The Sunflower Lemma of Erd\u00f6s and Rado asserts that a set of size at least $1 + k!(t-1)^k$ of elements of rank $k$ in a Boolean Lattice contains a sunflower of size $t$.  We develop counterparts of the Sunflower Lemma for distributive lattices, graphic matroids, and matroids representable over a fixed finite field.  We also show that there is no counterpart for arbitrary matroids.<\/jats:p>","DOI":"10.37236\/1963","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:08:31Z","timestamp":1578719311000},"source":"Crossref","is-referenced-by-count":0,"title":["Sunflowers in Lattices"],"prefix":"10.37236","volume":"12","author":[{"given":"Geoffrey","family":"McKenna","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,11,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r66\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r66\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:39:39Z","timestamp":1579322379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r66"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1963","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,11,29]]},"article-number":"R66"}}