Spreading linear triple systems and expander triple systems

Characterization of affine Steiner triple systems and Hall triple systems

It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner Electronic Notes in Discrete Mathematics 29 (2007) 17–21 1571-0653/$ – see front matter © 2007 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.07.004 triple system is affine if and on...

Embedding Steiner triple systems in hexagon triple systems

Directed Triple Systems

Directed triple systems are an example of block designs on directed graphs. A block design on a directed graph can be defined as follows. Let G be a directed graph of k vertices which contain no loops. Let S be a set of v elements. A collection of k-subsets of S with an assignment of the elements of each k-subset to the vertices of G is called a block design on G of order v if the following is ...

Sarvate – Beam Triple Systems

A Sarvate–Beam Triple System SB(v, 3) is a set V of v elements and a collection of 3–subsets of V such that each distinct pair of elements in V occurs in i blocks, for every i in the list 1, 2, . . . , ( v 2 ) . In this paper, we completely enumerate all Sarvate-Beam Triple Systems for v = 5 and v = 6. (In the case v = 5, we extend a previous result of R. Stanton [8].) 1 Sarvate–Beam Designs Th...

Perfect dexagon triple systems

We completely determine the spectrum for perfect dexagon triple systems. © 2007 Elsevier B.V. All rights reserved.