On Segre's Lemma of Tangents

Segre's lemma of tangents dates back to the 1950's when he used it in the proof of his "arc is a conic" theorem. Since then it has been used as a tool to prove results about various objects including internal nuclei, Kakeya sets, sets with few odd secants and further results on arcs. Here, we survey some of these results and report on how re-formulations of Segre's lemma of tangents are leading to new results

Arcs and Ovals in the Hermitian and Ree Unitals

The hermitian unitals U(q) and the Ree unitals RU(q) are examined for the existence of ovals and arcs. It is shown that U(q) does not have ovals for q > 2 and that RU(q), like U(q), is embedded in a much larger design with block intersections of cardinality ⩽ 2. Arcs of size 3q + 1 are constructed for the Ree unitals RU(q); they are ovals only in the case q = 3. In this case, U(3) and RU(3) are embedded in the same design and its automorphism group, the symplectic group Sp(6, 2), contains the automorphism groups of both the unitals; the coding-theoretic aspects are elucidated

Informe bibliomètric bimestral Campus Baix Llobregat. Base de dades Scopus. Juliol-agost 2018

Informe bibliomètric bimestral Campus Baix Llobregat. Base de dades Scopus. Data de la cerca 31/08/2018Postprint (author's final draft

Monomial hyperovals in Desarguesian planes

Thesis (M.Sc.) -- University of Adelaide, Dept. of Pure Mathematics, 199