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Large sets of subspace designs

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