{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:11:23Z","timestamp":1773447083665,"version":"3.50.1"},"reference-count":0,"publisher":"Combinatorial Press","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>Two binary structures \\(\\mathfrak{R}\\) and \\(\\mathfrak{R\u2019}\\) on the same vertex set \\(V\\) are \\((\\leq k)\\)-hypomorphic for a positive integer \\(k\\) if, for every set \\(K\\) of at most \\(k\\) vertices, the two binary structures induced by \\(\\mathfrak{R}\\) and \\(\\mathfrak{R\u2019}\\) on \\(K\\) are isomorphic. A binary structure \\(\\mathfrak{R}\\) is \\((\\leq k)\\)-reconstructible if every binary structure \\(\\mathfrak{R\u2019}\\) that is \\((\\leq k)\\)-hypomorphic to \\(\\mathfrak{R}\\) is isomorphic to \\(\\mathfrak{R}\\). In this paper, we describe the pairs of \\((\\leq 3)\\)-hypomorphic posets and the pairs of \\((\\leq 3)\\)-hypomorphic bichains. As a consequence, we characterize the \\((\\leq 3)\\)-reconstructible posets and the \\((\\leq 3)\\)-reconstructible bichains. This answers a question suggested by Y. Boudabbous and C. Delhomm\u00e9 during a personal communication.<\/jats:p>","DOI":"10.61091\/ars158-08","type":"journal-article","created":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:20Z","timestamp":1713134000000},"page":"67-79","source":"Crossref","is-referenced-by-count":1,"title":["Description of the \\((\\leq 3)\\)-hypomorphic Posets and Bichains. Application to the \\((\\leq 3)\\)-reconstruction"],"prefix":"10.61091","volume":"158","author":[{"name":"Faculty of Science of Sfax, Department of Mathematics Soukra Road km 4, PO Box 802, 3018 Sfax, Tunisia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamza Ben","family":"Brahim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed Y.","family":"Sayar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Faculty of Science of Sfax, Department of Mathematics Soukra Road km 4, PO Box 802, 3018 Sfax, Tunisia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:28Z","timestamp":1713134008000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-158\/description-of-the-leq-3-hypomorphic-posets-and-bichains-application-to-the-leq-3-reconstruction\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2024,3,31]]},"published-print":{"date-parts":[[2024,3,31]]}},"URL":"https:\/\/doi.org\/10.61091\/ars158-08","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1]]}}}