## 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
)

## Related URLs

## 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 |