{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:09:14Z","timestamp":1753880954423,"version":"3.41.2"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:p> Given sets [Formula: see text] and [Formula: see text], a labeled 2-structure is a function [Formula: see text] from [Formula: see text] to [Formula: see text]. The set [Formula: see text] is called the vertex set of [Formula: see text] and denoted by [Formula: see text]. The label set of [Formula: see text] is the set [Formula: see text] of [Formula: see text] such that [Formula: see text] for some [Formula: see text]. Given [Formula: see text], the 2-substructure [Formula: see text] of [Formula: see text] is denoted by [Formula: see text]. The dual [Formula: see text] of [Formula: see text] is defined on [Formula: see text] as follows. For distinct [Formula: see text], [Formula: see text]. A labeled 2-Structure [Formula: see text] is reversible provided that for [Formula: see text] such that [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text]. We only consider reversible labeled 2-structures whose vertex set is finite. <\/jats:p><jats:p> Let [Formula: see text] and [Formula: see text] be 2-structures such that [Formula: see text]. Given [Formula: see text], [Formula: see text] and [Formula: see text] are [Formula: see text]-hemimorphic if for every [Formula: see text] such that [Formula: see text], [Formula: see text] is isomorphic to [Formula: see text] or [Formula: see text]. Furthermore, let [Formula: see text] be a 2-structure. Given [Formula: see text], [Formula: see text] is [Formula: see text]-forced if [Formula: see text] and [Formula: see text] are the only 2-structures [Formula: see text]-hemimorphic to [Formula: see text]. We characterize the [Formula: see text]-forced 2-structures. Last, we provide a large class of [Formula: see text]-forced 2-structures. <\/jats:p>","DOI":"10.1142\/s1793830923500866","type":"journal-article","created":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T01:41:41Z","timestamp":1695260501000},"source":"Crossref","is-referenced-by-count":0,"title":["The 3-forced 2-structures"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3977-6346","authenticated-orcid":false,"given":"Abderrahim","family":"Boussa\u00efri","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Fondamentales et Appliqu\u00e9es, Facult\u00e9 des Sciences A\u00efn Chock, Hassan II University of Casablanca, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2625-504X","authenticated-orcid":false,"given":"Pierre","family":"Ille","sequence":"additional","affiliation":[{"name":"Aix Marseille University, CNRS, I2M, Marseille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,10,18]]},"reference":[{"key":"S1793830923500866BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.07.015"},{"key":"S1793830923500866BIB003","first-page":"14","volume":"112","author":"Boussa\u00efri A.","year":"2013","journal-title":"Ars Combin."},{"key":"S1793830923500866BIB004","first-page":"125","volume":"317","author":"Boussa\u00efri A.","year":"1993","journal-title":"C. 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