Current Search: Factorial experiment designs. (x)


Title

New Geometric Large Sets.

Creator

Hurley, Michael Robert, Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences

Abstract/Description

Let V be an ndimensional vector space over the field of q elements. By a geometric t[q^n, k, λ] design we mean a collection D of kdimensional subspaces of V, called blocks, such that every tdimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t[q^n, k, λ] designs that partitions [V K], the collection of kdimensional subspaces of V. In this work we construct nonisomorphic large sets using...
Show moreLet V be an ndimensional vector space over the field of q elements. By a geometric t[q^n, k, λ] design we mean a collection D of kdimensional subspaces of V, called blocks, such that every tdimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t[q^n, k, λ] designs that partitions [V K], the collection of kdimensional subspaces of V. In this work we construct nonisomorphic large sets using methods based on incidence structures known as the KramerMesner matrices. These structures are induced by particular group actions on the collection of subspaces of the vector space V. Subsequently, we discuss and use computational techniques for solving certain linear problems of the form AX = B, where A is a large integral matrix and X is a {0,1} solution. These techniques involve (i) lattice basisreduction, including variants of the LLL algorithm, and (ii) linear programming. Inspiration came from the 2013 work of Braun, Kohnert, Ostergard, and Wassermann, [17], who produced the first nontrivial large set of geometric designs with t ≥ 2. Bal Khadka and Michael Epstein provided the knowhow for using the LLL and linear programming algorithms that we implemented to construct the large sets.
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Date Issued

2016

PURL

http://purl.flvc.org/fau/fd/FA00004732, http://purl.flvc.org/fau/fd/FA00004732

Subject Headings

Group theory., Finite groups., Factorial experiment designs., Irregularities of distribution (Number theory), Combinatorial analysis.

Format

Document (PDF)