{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:38:03Z","timestamp":1773250683928,"version":"3.50.1"},"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 derive formulas for the ${\\bf cd}$-index and the toric $h$-vector of a convex polytope $P$ from a sweeping by a hyperplane.  These arise from interpreting the corresponding $S$-shelling of the dual of $P$.  We describe a partition of the faces of the complete truncation of $P$ to reflect explicitly the nonnegativity of its ${\\bf cd}$-index and what its components are counting.  One corollary is a quick way to compute the toric $h$-vector directly from the ${\\bf cd}$-index that turns out to be an immediate consequence of formulas of Bayer and Ehrenborg.  We also propose an \"extended toric\" $h$-vector that fully captures the information in the flag $h$-vector.<\/jats:p>","DOI":"10.37236\/553","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:52:09Z","timestamp":1578714729000},"source":"Crossref","is-referenced-by-count":1,"title":["Sweeping the ${\\bf cd}$-Index and the Toric $h$-Vector"],"prefix":"10.37236","volume":"18","author":[{"given":"Carl W.","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p66\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p66\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:15:03Z","timestamp":1579302903000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p66"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/553","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,24]]},"article-number":"P66"}}