Disjoint sets in projective planes of small order

Mustafa Gezek

Article Details

Disjoint sets in projective planes of small order

Authors:

Mustafa Gezek

Publisher:

Ankara University

Main Topics:

Mathematical Sciences

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 3, pp.803-814

Document Type:

Article

Publication Date:

9/2023

Document Language:

English

Document ID (Org No.):

2001299211

pISSN:

1303-5991

Keywords:

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.

 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.

 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.

 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.

Article Details

Disjoint sets in projective planes of small order

Authors: Mustafa Gezek

Publisher: Ankara University

Main Topics: Mathematical Sciences

Journal: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 3, pp.803-814

Document Type: Article

Publication Date: 9/2023

Document Language: English

Document ID (Org No.): 2001299211

pISSN: 1303-5991

Disjoint set

maximal arc

unital

Issues

Authors:

Mustafa Gezek

Publisher:

Ankara University

Main Topics:

Mathematical Sciences

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 3, pp.803-814

Document Type:

Article

Publication Date:

9/2023

Document Language:

English

Document ID (Org No.):

2001299211

pISSN:

1303-5991