Quasi-symmetric $2$-$(28,12,11)$ designs with an automorphism of order $5$

Kruc, Renata Vlahović; Krčadinac, Vedran

doi:10.3336/gm.58.2.01

Glasnik matematički, Vol. 58 No. 2, 2023.

Izvorni znanstveni članak

https://doi.org/10.3336/gm.58.2.01

Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$

Renata Vlahović Kruc ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Vedran Krčadinac ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

Puni tekst: engleski pdf 373 Kb

str. 159-166

preuzimanja: 209

citiraj

APA 6th Edition

Kruc, R.V. i Krčadinac, V. (2023). Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$ . Glasnik matematički, 58 (2), 159-166. https://doi.org/10.3336/gm.58.2.01

MLA 8th Edition

Kruc, Renata Vlahović i Vedran Krčadinac. "Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$ ." Glasnik matematički, vol. 58, br. 2, 2023, str. 159-166. https://doi.org/10.3336/gm.58.2.01. Citirano 07.04.2025.

Chicago 17th Edition

Kruc, Renata Vlahović i Vedran Krčadinac. "Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$ ." Glasnik matematički 58, br. 2 (2023): 159-166. https://doi.org/10.3336/gm.58.2.01

Harvard

Kruc, R.V., i Krčadinac, V. (2023). 'Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$ ', Glasnik matematički, 58(2), str. 159-166. https://doi.org/10.3336/gm.58.2.01

Vancouver

Kruc RV, Krčadinac V. Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$ . Glasnik matematički [Internet]. 2023 [pristupljeno 07.04.2025.];58(2):159-166. https://doi.org/10.3336/gm.58.2.01

IEEE

R.V. Kruc i V. Krčadinac, "Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$ ", Glasnik matematički, vol.58, br. 2, str. 159-166, 2023. [Online]. https://doi.org/10.3336/gm.58.2.01

Preuzmi JATS datoteku

Sažetak

A design is called quasi-symmetric if it has only two block intersection numbers.
Using a method based on orbit matrices, we classify quasi-symmetric $2$ - $(28, 12, 11)$
designs with intersection numbers $4$ , $6$ , and an automorphism of order $5$ . There
are exactly $31 696$ such designs up to isomorphism.

Ključne riječi

Quasi-symmetric design, automorphism group, orbit matrices

Hrčak ID:

312008

URI

https://hrcak.srce.hr/312008

Datum izdavanja:

7.4.2025.

Posjeta: 562 *

Podaci o članku

Publication date: 27 December 2023

Volume: Vol 58

Issue: Svezak 2

Pages: 159-166

DOI: 10.3336/gm.58.2.01

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Quasi-symmetric design, automorphism group, orbit matrices

Quasi-symmetric $2$ - $(28, 12, 11)$ designs with an automorphism of order $5$

Renata Vlahović Kruc[1]

Email: renata.vlahovic.kruc@math.hr

Vedran Krčadinac[2]

Email: vedran.krcadinac@math.hr

[1] Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

[2] Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

Abstract

A design is called quasi-symmetric if it has only two block intersection numbers. Using a method based on orbit matrices, we classify quasi-symmetric $2$ - $(28, 12, 11)$ designs with intersection numbers $4$ , $6$ , and an automorphism of order $5$ . There are exactly $31 696$ such designs up to isomorphism.

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