Naslov
Construction of transitive q-designs and q-graphs

Autori
Crnković, Dean ; Mikulić Crnković, Vedrana ; Švob, Andrea

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

Izvornik
Groups, graphs and everything in between / Malnič, Aleksander ; Potočnik, Primož ; Zgrablić, Boris ; Šparl, Primož ; Kutnar, Klavdija ; Zhang Pettersson, Sophia Cui ; Hujdurović, Ademir - Koper : Slovenian Discrete and Applied Mathematics Sociaty, 2023, 6-7

Skup
Groups, graphs and everything in between

Mjesto i datum
Bled, Slovenija, 04.05.2023. - 07.05.2023

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
q-analog ; strongly regular graph ; subspace design

Sažetak
The notion of q-analog of designs has been introduced by Delsarte [5]. In 1987, Thomas [6] constructed the first non-trivial q-analog of design with parameters 2-(n, 3, 7 ; 2) ; n > 6 ; n = 6k+1 or n = 6k-1. An important result was given in [2], where the authors constructed a design over a finite field with parameters 2-(13, 3, 1 ; 2) which was the first known example of a Steiner q-design that does not arise from spreads. Further, in [1] we introduced the notion of q-analog of strongly regular graphs. We will present the method of constructing transitive q-analogs of designs given in [4], as a generalization of the construction of transitive block designs presented in [3], as well as a method of constructing transitive q-analogs of graphs. References [1] M. Braun, D. Crnković, M. De Boeck, V. Mikulić Crnković, A. Švob, q-Analogs of strongly regular graphs, preprint, arXiv:2105.14525. [2] M. Braun, T. Etzion, P. Östergård, A. Vardy, A. Wassermann, Existence of q-analogs of Steiner systems, Forum of Math Pi 4:e7 (2016), 14 pages. [3] D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures constructed from the unitary group U(3, 3), J. Statist. Plann. Inference 144 (2014), 19{;40. [4] D. Crnković, V. Mikulić Crnković, A. Švob, Construction of transitive q-analogs of designs, Math. Comput. Sci. 17 (2023), Paper No. 2, 5 pages. [5] P. Delsarte, Association schemes and t-designs in regular semilattices. J. Comb. Theory Ser. A 20 (1976). [6] S. Thomas, Designs over finite fields, Geomet. Dedic. 24 (1987), 237{;242.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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