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; Weiner, Zsuzsa. - In: COMBINATORICA. - ISSN 0209-9683. - STAMPA. - 41:5(2021), pp. 601-623. [10.1007/s00493-020-4419-z]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
