{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835600,"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>In analogy to omittable lines in the plane, we initiate the study of omittable planes in $3$-space. Given a collection of $n$ planes in real projective $3$-space, a plane $\\Pi$ is said to be omittable if $\\Pi$ is free of ordinary lines of intersection \u2013 in other words, if all the lines of intersection of $\\Pi$ with other planes from the collection come at the intersection of three or more planes. We provide two infinite families of planes yielding omittable planes in either a pencil or near-pencil, together with examples having between three and seven omittable planes, examples that we call \"sporadic,\" which do not fit into either of the two infinite families.<\/jats:p>","DOI":"10.37236\/662","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:42:40Z","timestamp":1578696160000},"source":"Crossref","is-referenced-by-count":0,"title":["Omittable Planes"],"prefix":"10.37236","volume":"18","author":[{"given":"Branko","family":"Gr\u00fcnbaum","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Lenchner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,9,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p175\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p175\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:02:27Z","timestamp":1579284147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p175"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/662","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,9,2]]},"article-number":"P175"}}