{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T11:07:19Z","timestamp":1780744039652,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given a finite poset $\\mathcal{P}$, a family $\\mathcal{F}$ of elements in the Boolean lattice is induced-$\\mathcal{P}$-saturated if $\\mathcal{F}$ contains no copy of $\\mathcal{P}$ as an induced subposet but every proper superset of $\\mathcal{F}$ contains a copy of $\\mathcal{P}$ as an induced subposet.\u00a0 The minimum size of an induced-$\\mathcal{P}$-saturated family in the $n$-dimensional Boolean lattice, denoted $\\mathrm{sat}^*(n,\\mathcal{P})$, was first studied by Ferrara et al. (2017).\r\nOur work focuses on strengthening lower bounds. For the 4-point poset known as the diamond, we prove $\\mathrm{sat}^*(n,\\Diamond)\\geq\\sqrt{n}$, improving upon a logarithmic lower bound. For the antichain with $k+1$ elements, we prove $$\\mathrm{sat}^*(n,\\mathcal{A}_{k+1})\\geq \\left(1-\\frac{1}{\\log_2k}\\right)\\frac{kn}{\\log_2 k}$$ for $n$ sufficiently large, improving upon a lower bound of $3n-1$ for $k\\geq 3$.\u00a0<\/jats:p>","DOI":"10.37236\/8949","type":"journal-article","created":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:20:21Z","timestamp":1590718821000},"source":"Crossref","is-referenced-by-count":7,"title":["Improved Bounds for Induced Poset Saturation"],"prefix":"10.37236","volume":"27","author":[{"given":"Ryan R.","family":"Martin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Heather C.","family":"Smith","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shanise","family":"Walker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2020,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p31\/8087","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p31\/8087","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:20:21Z","timestamp":1590718821000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/8949","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,22]]},"article-number":"P2.31"}}