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On q-analogs of group divisible designs

Title data

de Beule, Jan ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On q-analogs of group divisible designs.
2019
Event: 9th Slovenian International Conference on Graph Theory , 23.-29.06.2019 , Bled, Slovenia.
(Conference item: Conference , Speech )

Abstract in another language

Group divsible designs are well-studied objects in combinatorics. Recently, q-analogs of group divisible designs (q-GDDs) have been introduced. Let v, g, k, and
λ be sets of positive integers and let be a positive integer. The q-analog of a group divisible design of index
λ and order v with parameters (v,g,k,λ)_q is a triple
(V,G,V), where V is a vector space of dimension v over GF(q), G is a partition of V into g -dimensional subspaces (groups), and V is a family of k-dimensional subspaces (blocks) of V such that every 2-dimensional subspace of V
occurs in exactly λ blocks or one group, but not both.
q-analogs of group divisible designs are connected to scattered subspaces in finite geometry, q-analogs of Steiner systems, subspace design packings and more.
After an introduction to the subject, recent results are presented with special attention on cases where the vector space partition is a non-Desarguesian spread. For example, there is no (8,4,4,7)_2 GDD and a (8,4,4,14)_2 GDD exists only for the Desarguesian spread.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: speaker: Alfred Wassermann
Keywords: group divisible designs; q-analogs; scattered subspaces; packing designs; divisible sets; Steiner systems
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 01 Jul 2019 08:42
Last Modified: 01 Jul 2019 08:42
URI: https://eref.uni-bayreuth.de/id/eprint/49765