{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:36:53Z","timestamp":1760524613517,"version":"3.41.2"},"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>For many well-known families of triple systems $\\mathcal{M}$, there are perhaps many near-extremal $\\mathcal{M}$-free configurations that are far from each other in edit-distance. Such a property is called non-stable and is a fundamental barrier to determining the Tur\u00e1n number of $\\mathcal{M}$. Liu and Mubayi gave the first finite example that is non-stable. In this paper, we construct another finite family of triple systems $\\mathcal{M}$ such that there are two near-extremal $\\mathcal{M}$-free configurations that are far from each other in edit-distance. We also prove its Andr\u00e1sfai-Erd\u0151s-S\u00f3s type stability theorem: Every $\\mathcal{M}$-free triple system whose minimum degree is close to the average degree of the extremal configurations is a subgraph of one of these two near-extremal configurations. As a corollary, our main result shows that the boundary of the feasible region of $\\mathcal{M}$ has exactly two global maxima.<\/jats:p>","DOI":"10.37236\/11701","type":"journal-article","created":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T08:18:04Z","timestamp":1713428284000},"source":"Crossref","is-referenced-by-count":3,"title":["A 2-Stable Family of Triple Systems"],"prefix":"10.37236","volume":"31","author":[{"given":"Yixiao","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Hou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heng","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,4,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i2p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i2p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T08:18:05Z","timestamp":1713428285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i2p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/11701","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,4,5]]},"article-number":"P2.3"}}