{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:59Z","timestamp":1753893839392,"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>The augmented Bergman complex of a matroid is a simplicial complex introduced recently in work of Braden, Huh, Matherne, Proudfoot and Wang.\u00a0 It may be viewed as a hybrid of two well-studied pure shellable simplicial complexes associated to matroids: the independent set complex and Bergman complex.\r\nIt is shown here that the augmented Bergman complex is also shellable, via two different families of shelling orders.\u00a0 Furthermore, comparing the description of its homotopy type induced from the two shellings re-interprets a known convolution formula counting bases of the matroid. The representation of the automorphism group of the matroid on the homology of the augmented Bergman complex turns out to have a surprisingly simple description. This last fact is generalized to closures beyond those coming from a matroid.<\/jats:p>","DOI":"10.37236\/10739","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T12:19:09Z","timestamp":1645705149000},"source":"Crossref","is-referenced-by-count":1,"title":["Topology of Augmented Bergman Complexes"],"prefix":"10.37236","volume":"29","author":[{"given":"Elisabeth","family":"Bullock","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aidan","family":"Kelley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Reiner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin","family":"Ren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gahl","family":"Shemy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dawei","family":"Shen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brian","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhichun Joy","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,2,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T12:19:10Z","timestamp":1645705150000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i1p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1,27]]}},"URL":"https:\/\/doi.org\/10.37236\/10739","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,2,25]]},"article-number":"P1.31"}}