Simple Non-trivial Designs with an Arbitrary Automorphism Group

Simple Non-trivial Designs with an Arbitrary Automorphism Group

For positive integers t; v; k and l satisfying k > t and v > k; a t-design D with parameters ðv; k; lÞ is a set X of v points, together with a collectionB of subsets, called blocks, such that each block contains exactly k points and each t-tuple of points is contained in exactly l blocks. A t ðv; k; lÞ design is simple if repeated blocks are not allowed and is non-trivial if not all k-sets of p...

The Simple 7-(33,8,10)-Designs with Automorphism Group PΓL(2,32)

Lattice basis reduction in combination with an efficient backtracking algorithm is used to find all (4 996 426) simple 7(33,8,10) designs with automorphism group PΓL(2,32). The paper contains a short description of the algorithm.

Non-moishezon Twistor Spaces of 4cp with Non-trivial Automorphism Group

We show that a twistor space of a self-dual metric on 4CP with U(1)-isometry is not Moishezon iff there is a C∗-orbit biholomorphic to a smooth elliptic curve, where the C∗-action is the complexification of the U(1)action on the twistor space. It follows that the U(1)-isometry has a two-sphere whose isotropy group is Z2. We also prove the existence of such twistor spaces in a strong form to sho...

The Discovery of Simple 7-Designs with Automorphism Group PTL (2, 32)

A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endowed with graphical interface modules. Standard applications can be run automatically whereas research projects mostly require small C or C++ programs. The basic philosophy behind the system is to transform problems int...

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group Or a Unitary Group