{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:31Z","timestamp":1759335811818,"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>We extend Crapo's $\\beta $ invariant from matroids to greedoids, concentrating especially on antimatroids.  Several familiar expansions for $\\beta (G)$ have greedoid analogs.  We give combinatorial interpretations for $\\beta (G)$ for simplicial shelling antimatroids associated with chordal graphs.  When $G$ is this antimatroid and $b(G)$ is the number of blocks of the chordal graph $G$, we prove $\\beta (G)=1-b(G)$.<\/jats:p>","DOI":"10.37236\/1298","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:53:52Z","timestamp":1578689632000},"source":"Crossref","is-referenced-by-count":3,"title":["A $\\beta$ Invariant for Greedoids and Antimatroids"],"prefix":"10.37236","volume":"4","author":[{"given":"Gary","family":"Gordon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1997,3,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T01:14:05Z","timestamp":1579310045000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v4i1r13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,3,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1997,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1298","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1997,3,28]]},"article-number":"R13"}}