In this paper, we generalize the so-called Korchmáros-Mazzocca arcs, that is, point sets of size q + t intersecting each line in 0, 2 or t points in a finite projective plane of order q. For t ≠ 2, this means that each point of the point set is incident with exactly one line meeting the point set in t points. In PG(2,p^n), we change 2 in the definition above to any integer m and describe all examples when m or t is not divisible by p. We also study mod p variants of these objects, give examples and under some conditions we prove the existence of a nucleus.

Generalizing Korchmáros-Mazzocca Arcs

Csajbok, Bence;
2021-01-01

Abstract

In this paper, we generalize the so-called Korchmáros-Mazzocca arcs, that is, point sets of size q + t intersecting each line in 0, 2 or t points in a finite projective plane of order q. For t ≠ 2, this means that each point of the point set is incident with exactly one line meeting the point set in t points. In PG(2,p^n), we change 2 in the definition above to any integer m and describe all examples when m or t is not divisible by p. We also study mod p variants of these objects, give examples and under some conditions we prove the existence of a nucleus.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/234051
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