{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:54Z","timestamp":1753893774270,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The maximal and next-to-maximal subspaces of a nonsingular parabolic quadric $Q(2n,2)$, $n \\geq 2$, which are not contained in a given hyperbolic quadric $Q^+(2n-1,2) \\subset Q(2n,2)$ define a sub near polygon ${\\Bbb I}_n$ of the dual polar space $DQ(2n,2)$. It is known that every valuation of $DQ(2n,2)$ induces a valuation of ${\\Bbb I}_n$. In this paper, we classify all valuations of the near octagon ${\\Bbb I}_4$ and show that they are all induced by a valuation of $DQ(8,2)$. We use this classification to show that there exists up to isomorphism a unique isometric full embedding of ${\\Bbb I}_n$ into each of the dual polar spaces $DQ(2n,2)$ and $DH(2n-1,4)$.<\/jats:p>","DOI":"10.37236\/1102","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:58:50Z","timestamp":1578700730000},"source":"Crossref","is-referenced-by-count":1,"title":["The Valuations of the Near Octagon ${\\Bbb I}_4$"],"prefix":"10.37236","volume":"13","author":[{"given":"Bart","family":"De Bruyn","sequence":"first","affiliation":[]},{"given":"Pieter","family":"Vandecasteele","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r76\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r76\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:08:11Z","timestamp":1579302491000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r76"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1102","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,8,25]]},"article-number":"R76"}}