Disjoint sets in projective planes of small order

Mustafa Gezek

Makale detayları

Disjoint sets in projective planes of small order

Yazarlar:

Mustafa Gezek

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

9/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001299211

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 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.

Makale detayları

Disjoint sets in projective planes of small order

Yazarlar: Mustafa Gezek

Yayıncı: Ankara University

Ana Başlıklar: Mathematical Sciences

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

Belge Tipi: Makale

Yayın Tarihi: 9/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001299211

pISSN: 1303-5991

Disjoint set

maximal arc

unital

Sayı

Yazarlar:

Mustafa Gezek

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

9/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001299211

pISSN:

1303-5991