{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:45:05Z","timestamp":1758476705571,"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>Let $I\\subset K[x_1,\\ldots,x_n]$ be\u00a0 a zero-dimensional monomial ideal, and $\\Delta(I)$ be the simplicial complex whose Stanley--Reisner ideal is the polarization of $I$. It follows from a result of Soleyman Jahan that $\\Delta(I)$ is shellable. We give a new short proof of this fact by providing an explicit shelling. Moreover, we show that\u00a0 $\\Delta(I)$ is even vertex decomposable.\u00a0The ideal $L(I)$, which is defined to be the Stanley--Reisner ideal of the Alexander dual of $\\Delta(I)$, has a linear resolution which is cellular and supported on a regular CW-complex. All powers of $L(I)$ have a linear resolution. We compute $\\mathrm{depth}\\ L(I)^k$ and show that $\\mathrm{depth}\\ L(I)^k=n$ for all $k\\geq n$.<\/jats:p>","DOI":"10.37236\/4894","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:26:02Z","timestamp":1578684362000},"source":"Crossref","is-referenced-by-count":0,"title":["Simplicial Complexes of Whisker Type"],"prefix":"10.37236","volume":"22","author":[{"given":"Mina","family":"Bigdeli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Herzog","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takayuki","family":"Hibi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Macchia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,3,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p75\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p75\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:23:26Z","timestamp":1579238606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p75"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4894","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,3,23]]},"article-number":"P1.75"}}