{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,16]],"date-time":"2025-11-16T02:26:21Z","timestamp":1763259981122,"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>Recently, a lower bound on the size of linear sets in projective spaces intersecting a hyperplane in a canonical subgeometry was established. There are several constructions showing that this bound is tight. In this paper, we generalize this bound to linear sets meeting some subspace $\\pi$ in a canonical subgeometry. We obtain a tight lower bound on the size of any ${\\mathbb F}_{q}$-linear set spanning $\\mathrm{PG}(d,q^n)$ in case that $n \\leq q$ and $n$ is prime. We also give constructions of linear sets attaining equality in the former bound, both in the case that $\\pi$ is a hyperplane, and in the case that $\\pi$ is a lower dimensional subspace.<\/jats:p>","DOI":"10.37236\/12424","type":"journal-article","created":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T12:33:01Z","timestamp":1732797181000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Minimum Size of Linear Sets"],"prefix":"10.37236","volume":"31","author":[{"given":"Sam","family":"Adriaensen","sequence":"first","affiliation":[]},{"given":"Paolo","family":"Santonastaso","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,11,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T12:33:01Z","timestamp":1732797181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,29]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12424","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,11,29]]},"article-number":"P4.52"}}