{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:11Z","timestamp":1753893851588,"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>In this paper results are proved with applications to the orbits of $(n-1)$-dimensional subspaces disjoint from a regulus $\\mathcal{R}$ of $(n-1)$-subspaces in\u00a0$\\mathrm{PG}(2n-1,q)$, with respect to the subgroup of $\\mathrm{PGL}(2n,q)$ fixing $\\mathcal{R}$.\u00a0Such results have consequences on several aspects of finite geometry.\u00a0First of all, a necessary condition for an $(n-1)$-subspace $U$ and a regulus $\\mathcal{R}$ of $(n-1)$-subspaces to be extendable to a Desarguesian spread is given.\u00a0The description also allows to improve results of Barwick and Jackson\u00a0on the Andr\u00e9 -Bruck-Bose representation of a $q$-subline in $\\mathrm{PG}(2,q^n)$. Furthermore, the results in this paper are applied to the classification of linear sets, in particular clubs.<\/jats:p>","DOI":"10.37236\/4662","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:52:56Z","timestamp":1578693176000},"source":"Crossref","is-referenced-by-count":1,"title":["Subspaces Intersecting Each Element of a Regulus in One Point, Andr\u00e9-Bruck-Bose Representation and Clubs"],"prefix":"10.37236","volume":"23","author":[{"given":"Michel","family":"Lavrauw","sequence":"first","affiliation":[]},{"given":"Corrado","family":"Zanella","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,2,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:36:00Z","timestamp":1579239360000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/4662","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,2,19]]},"article-number":"P1.37"}}