- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Cilt: 72 Sayı: 3
- Disjoint sets in projective planes of small order
Disjoint sets in projective planes of small order
Authors : Mustafa Gezek
Pages : 803-814
Doi:10.31801/cfsuasmas.1194816
View : 21 | Download : 35
Publication Date : 2023-09-30
Article Type : Research
Abstract :In this paper, results of a computer search for disjoint sets associated with maximal arcs and unitals in projective planes of order 16, and disjoint sets associated with unitals in projective planes of orders 9 and 25 are reported. It is shown that the number of pairs of disjoint unitals in planes of order 9 is exactly four, and new pairs and triples of disjoint degree 4 maximal arcs are shown to exist in some of the planes of order 16. New bounds on the number of 104-sets of type (4, 8) and 156-sets of type (8, 12) are achieved. A combinatorial method for finding new maximal arcs, new unitals, and new v-sets of type (m, n) is introduced. All disjoint sets found in this study are explicitly listed.Keywords : Disjoint set, maximal arc, unital