Naslov
Symmetric Associated Schemes and Finite Geometries

Autori
Martinjak, Ivica

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
20th Scientific-Professional Colloquium on Geometry and Graphics / T. Došlić, E. Jurkin - , 2017, 23-23

Skup
20th Scientific-Professional Colloquium on Geometry and Graphics

Mjesto i datum
Fužine, Hrvatska, 03.09.2017. - 07.09.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
finite geometry, projective plane, association scheme, Bose-Mesner algebra, biplane, automorphism group

Sažetak
Let ${;\cal B};$ be a nontrivial biplane of order $k-2$ represented by symmetric canonical incidence matrix with trace equal to $1+ \binom{;k};{;2};$. We prove that ${;\cal B};$ includes a partially balanced incomplete block design with 3-class association scheme. Consequently, these structures are symmetric, having $2k-6$ points. We also present some representatives of this class of symmetric association schemes. In addition we efficiently construct four biplanes of order 9 - except the one with the smallest automorphism group

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA