Unitals in projective planes of order 16

Basit Öğe Kaydı
dc.authorid0000-0001-5488-9341
dc.authorid0000-0002-6217-460X
dc.authorscopusid6602721377
dc.authorscopusid57201668033
dc.authorwosidGezek, Mustafa/AAW-3807-2020
dc.contributor.authorStoichev, Stoicho Dimitrov
dc.contributor.authorGezek, Mustafa
dc.date.accessioned2022-05-11T14:32:18Z
dc.date.available2022-05-11T14:32:18Z
dc.date.issued2021
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractIn this study, we perform computer searches for unitals in planes of order 16. The number of known nonisomorphic unitals in these planes is improved to be 261. Some data related to 2- (65, 5, 1) designs associated with unitals are given. New lower bounds on the number of unital designs in projective planes of order 16 and 2- (65, 5, 1) designs are established. The computations show that thirty-nine unitals can be embedded in two or more nonisomorphic projective planes of order 16. Fifteen new connections between planes of order 16 (based on unitals) are found. All unitals found by the algorithms used in this study are explicitly listed. We assume familiarity with the basic facts from combinatorial design theory and finite geometries [5, 9, 16]. A t-(v, k, ?) design (t-design) is a pair D = {X, B} of a set X of cardinality v, called points, and a collection B of k-subsets of X, called blocks, such that every t points appear together in exactly ? blocks. A 2-design with ? = 1 is called a Steiner design. The incidence matrix of a 2-(v, k, ?) design D is a matrix M = (mij) with rows labeled by the blocks of D, columns labeled by the points of D, where mi,j = 1 if the ith block contains the j th point and mi,j = 0 otherwise. For a prime p, the rank of the incidence matrix of design D over a finite field of characteristic p is called the p-rank of D. Two designs D and D? are called isomorphic if there is a bijection between their point sets that maps
dc.identifier.doi10.3906/mat-2008-46
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85103731479
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.3906/mat-2008-46
dc.identifier.urihttps://hdl.handle.net/20.500.11776/7451
dc.identifier.volume45
dc.identifier.wosWOS:000634389600027
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorGezek, Mustafa
dc.language.isoen
dc.publisherScientific Technical Research Council Turkey-Tubitak
dc.relation.ispartofTurkish Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectUnital
dc.subjectprojective plane
dc.subjectSteiner design
dc.subjectgraph isomorphism
dc.subjectorbits
dc.subjectautomorphism group
dc.subjectBuekenhout-Metz Unitals
dc.subjectDesigns
dc.titleUnitals in projective planes of order 16
dc.typeArticle

Dosyalar

Orijinal paket
Listeleniyor 1 - 1 / 1
Küçük Resim
İsim:
7451.pdf
Boyut:
218.95 KB
Biçim:
Adobe Portable Document Format
Açıklama:
Tam Metin / Full Text
İndir

Koleksiyon

WoS İndeksli Yayınlar Koleksiyonu
Fen Edebiyat Fakültesi Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu
TR-Dizin İndeksli Yayınlar Koleksiyonu