2014/11/26 by Braun, Michael, Kiermaier, Michael, Kohnert, Axel +1
#05B25 #11Txx #Combinatorics (math.CO) #FOS: Mathematics #Primary 51E20 #Secondary 05B05
paper · doi:10.48550/arxiv.1411.7181
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 LS5[2](2,3,6). The application of the new recursion method to this halving and an already known LS3[2](2,3,6) yields two infinite two-parameter series of halvings LS3[2](2,k,v) and LS5[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.