Advanced search options

You searched for `subject:(Candelabra system)`

. One record found.

▼ Search Limiters

1. Balachandran, Niranjan. The 3-Design Problem.

Degree: PhD, Mathematics, 2008, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1211922186

This dissertation studies the ‘asymptotic
existence’ conjecture for 3-designs with the primary goal of
constructing new families of 3-designs. More specifically, this
dissertation includes the following: Firstly, by
considering the action of the group PSL(2,q) on the finite
projective line and the orbits of the action of this group to
construct simple 3-designs. While the case q congruent to 3 modulo
4 is 3-homogeneous (so that orbits of any ‘base’ block’ would yield
designs), the case q congruent to 1 modulo 4 does not work the same
way. We overcome some of these issues by considering appropriate
unions of orbits to produce new infinite families of 3-designs with
PSL(2,q) acting as a group of automorphisms. We also prove that our
constructions actually produce an abundance of simple 3-designs for
any block size if q is sufficiently large and also construct a
large set of Divisible designs as an application of our
constructions. We generalize the notion of a
Candelabra system to more general structures, called Rooted Forest
Set systems and prove a few general results on combinatorial
constructions for these general set structures. Then, we specialize
to the case of k=6 and extend a theorem of Hanani to produce new
infinite families of Steiner 3-designs with block size
6. Finally, we consider Candelabra systems and
prove that a related incidence matrix has full row rank over the
rationals. This leads to interesting possibilities for ‘lambda
large’ theorems for Candelabra systems. While a ‘lambda large’
theorem for Candelabra systems do not directly yield any Steiner
3-design, it allows for constructions of new Steiner 3-designs on
large sets using methods such as Block
spreading.
*Advisors/Committee Members: Robertson, Neil (Advisor).*

Subjects/Keywords: Mathematics; 3-design; Candelabra system; projective special linear groups

…application of our
constructions.
2. We generalize the notion of a *Candelabra* *system* to more general… …block size 6.
3. Finally, we consider *Candelabra* systems and prove that a related incidence… …for *Candelabra* systems. While a λ-large theorem for *Candelabra* systems do not directly yield… …arXiv.org :math/0611842v1),
2006.
3. “New infinite families of *Candelabra* Systems with block… …size 6 and stem size 2
”, submitted, 2007.
4. “ A λ-large theorem for *Candelabra* Systems”, in…

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Balachandran, N. (2008). The 3-Design Problem. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1211922186

Chicago Manual of Style (16^{th} Edition):

Balachandran, Niranjan. “The 3-Design Problem.” 2008. Doctoral Dissertation, The Ohio State University. Accessed October 28, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1211922186.

MLA Handbook (7^{th} Edition):

Balachandran, Niranjan. “The 3-Design Problem.” 2008. Web. 28 Oct 2020.

Vancouver:

Balachandran N. The 3-Design Problem. [Internet] [Doctoral dissertation]. The Ohio State University; 2008. [cited 2020 Oct 28]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1211922186.

Council of Science Editors:

Balachandran N. The 3-Design Problem. [Doctoral Dissertation]. The Ohio State University; 2008. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1211922186