{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819930,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A triple $(\\mathcal{S},S,\\mathcal{Q})$ consisting of a near polygon $\\mathcal{S}$, a line spread $S$ of $\\mathcal{S}$ and a set $\\mathcal{Q}$ of quads of $\\mathcal{S}$ is called a polygonal triple\u00a0if certain nice properties are satisfied, among which there is the requirement that the point-line geometry $\\mathcal{S}'$ formed by the lines of $S$ and the quads of $\\mathcal{Q}$ is itself also a near polygon. This paper addresses the problem of classifying all near polygons $\\mathcal{S}$ that admit a polygonal triple $(\\mathcal{S},S,\\mathcal{Q})$ for which a given generalized polygon $\\mathcal{S}'$ is the associated near polygon. We obtain several nonexistence results and show that the $G_2(4)$ and $L_3(4)$ near octagons are the unique near octagons that admit polygonal triples whose quads are isomorphic to the generalized quadrangle $W(2)$ and whose associated near polygons are respectively isomorphic to the dual split Cayley hexagon $H^D(4)$ and the unique generalized hexagon of order $(4,1)$.<\/jats:p>","DOI":"10.37236\/8476","type":"journal-article","created":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T10:53:34Z","timestamp":1634813614000},"source":"Crossref","is-referenced-by-count":0,"title":["Characterizations of the $G_2(4)$ and $L_3(4)$ Near Octagons"],"prefix":"10.37236","volume":"28","author":[{"given":"Bart","family":"De Bruyn","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,10,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T10:53:34Z","timestamp":1634813614000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i4p12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,22]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,8]]}},"URL":"https:\/\/doi.org\/10.37236\/8476","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,10,22]]},"article-number":"P4.12"}}