## 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
)

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## 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.