{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:15Z","timestamp":1753893855830,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>It follows by Bixby's Lemma that if $e$ is an element of a $3$-connected matroid $M$, then either $\\textrm{co}(M\\backslash e)$, the cosimplification of $M\\backslash e$, or $\\textrm{si}(M\/e)$, the simplification of $M\/e$, is $3$-connected. A natural question to ask is whether $M$ has an element $e$ such that both $\\textrm{co}(M\\backslash e)$ and $\\textrm{si}(M\/e)$ are $3$-connected. Calling such an element \"elastic\", in this paper we show that if $|E(M)|\\ge 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans.<\/jats:p>","DOI":"10.37236\/9919","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T01:56:28Z","timestamp":1625018188000},"source":"Crossref","is-referenced-by-count":0,"title":["Elastic Elements in 3-Connected Matroids"],"prefix":"10.37236","volume":"28","author":[{"given":"George","family":"Drummond","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zach","family":"Gershkoff","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Susan","family":"Jowett","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles","family":"Semple","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jagdeep","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,6,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T01:56:29Z","timestamp":1625018189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i2p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,18]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9919","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,6,18]]},"article-number":"P2.39"}}