{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:31:18Z","timestamp":1774625478092,"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>For a simplicial complex $\\Delta$, the graded Betti number $\\beta_{i,j}({\\bf k}[\\Delta])$ of the Stanley-Reisner ring ${\\bf k}[\\Delta]$ over a field ${\\bf k}$ has a combinatorial interpretation due to Hochster. Terai and Hibi showed that if $\\Delta$ is the boundary complex of a $d$-dimensional stacked polytope with $n$ vertices for $d\\geq3$, then $\\beta_{k-1,k}({\\bf k}[\\Delta])=(k-1){n-d\\choose k}$. We prove this combinatorially.<\/jats:p>","DOI":"10.37236\/281","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:19:29Z","timestamp":1578698369000},"source":"Crossref","is-referenced-by-count":5,"title":["A Combinatorial Proof of a Formula for Betti Numbers of a Stacked Polytope"],"prefix":"10.37236","volume":"17","author":[{"given":"Suyoung","family":"Choi","sequence":"first","affiliation":[]},{"given":"Jang Soo","family":"Kim","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,1,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T19:02:44Z","timestamp":1579287764000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/281","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1,5]]},"article-number":"R9"}}