## Title data

Braun, Michael ; Kiermaier, Michael ; Kohnert, Axel ; Laue, Reinhard:

**Large sets of subspace designs.**

*In:* Journal of Combinatorial Theory, Series A.
Vol. 147
(April 2017)
.
- pp. 155-185.

ISSN 0097-3165

DOI: https://doi.org/10.1016/j.jcta.2016.11.004

## Abstract in another language

In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Graßmannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to subspace designs.

We construct a 2-(6,3,78)_5 design by computer, which corresponds to a halving LS_5[2](2,3,6). The application of the new recursion method to this halving and an already known LS_3[2](2,3,6) yields two infinite two-parameter series of halvings LS_3[2](2,k,v) and LS_5[2](2,k,v) with integers v => 6, v == 2 (mod 4), and 3 <= k <= v-3, k == 3 ( mod 4).

Thus in particular, two new infinite series of nontrivial subspace designs with t=2 are constructed. Furthermore as a corollary, we get the existence of infinitely many nontrivial large sets of subspace designs with t=2.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | q-analog; combinatorial design; subspace design; large set; halving |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 04 May 2017 11:07 |

Last Modified: | 04 May 2017 11:07 |

URI: | https://eref.uni-bayreuth.de/id/eprint/36946 |