Tight sets and m-ovoids of generalised quadrangles

John Bamberg, Maska Law, Tim Penttila

    Research output: Contribution to journalArticle

    25 Citations (Scopus)

    Abstract

    The concept of a tight set of points of a generalised quadrangle was introduced by S. E. Payne in 1987, and that of an m-ovoid of a generalised quadrangle was introduced by J. A. Thas in 1989, and we unify these two concepts by defining intriguing sets of points. We prove that every intriguing set of points in a generalised quadrangle is an m-ovoid or a tight set, and we state an intersection result concerning these objects. In the classical generalised quadrangles, we construct new m-ovoids and tight sets. In particular, we construct m-ovoids of W(3,q), q odd, for all even m; we construct (q+1)/2-ovoids of W(3,q) for q odd; and we give a lower bound on m for m-ovoids of H(4,q 2).
    Original languageEnglish
    Pages (from-to)1-17
    JournalCombinatorica
    Volume29
    Issue number1
    DOIs
    Publication statusPublished - 2009

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