In this paper, we first determine the minimum possible size of an F q-linear set of rank k in PG(1,q n). We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q-linear set of rank k in PG(2,q n). In the case k=n, this confirms a conjecture by Sziklai in [9].

Original languageEnglish
Pages (from-to)109-124
Number of pages16
JournalJournal of Combinatorial Theory - Series A
Publication statusPublished - May 2019

    Research areas

  • Directions determined by a point set, Linear set, Linearised polynomial

ID: 44433585