{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:19:28Z","timestamp":1759940368824,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove that the external activity complex $\\textrm{Act}_&lt;(M)$ of a matroid is shellable. In fact, we show that every linear extension of LasVergnas's external\/internal order $&lt;_{ext\/int}$ on $M$ provides a shelling of $\\textrm{Act}_&lt;(M)$. We also show that every linear extension of LasVergnas's internal order $&lt;_{int}$ on $M$ provides a shelling of the independence complex $IN(M)$. As a corollary, $\\textrm{Act}_&lt;(M)$ and $M$ have the same $h$-vector.\u00a0We prove that, after removing its cone points, the external activity complex is contractible if $M$ contains $U_{1,3}$ as a minor, and a sphere otherwise.<\/jats:p>","DOI":"10.37236\/5042","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:47:38Z","timestamp":1578689258000},"source":"Crossref","is-referenced-by-count":1,"title":["The Topology of the External Activity Complex of a Matroid"],"prefix":"10.37236","volume":"23","author":[{"given":"Federico","family":"Ardila","sequence":"first","affiliation":[]},{"given":"Federico","family":"Castillo","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9 Alejandro","family":"Samper","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,7,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:27:03Z","timestamp":1579238823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,22]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5042","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,7,22]]},"article-number":"P3.8"}}