> < ^ Date: Tue, 07 Mar 1995 13:43:00 +0000
> < ^ From: Leonard Soicher <l.h.soicher@qmul.ac.uk >
< ^ Subject: Re: Design Theory package?

Tim Sturge writes:

I am using GAP to investigate the properties of some small geometric
structures, and I wonder if a design theory package or library has
been written for GAP.

Not to the best of my knowledge, but you should look at the GRAPE share
library package for computing with graphs with (possibly trivial) group
actions. Many of the algorithms in GRAPE were motivated by the desire
to study graphs related to finite geometries, such as incidence graphs
and collinearity graphs. You can study your design in GRAPE via its
incidence graph, and can, for example determine the automorphism group
of your design (using the function AutGroupGraph, which can determine
the subgroup of the automorphism group of a graph preserving a given
partition of the vertices).

If anyone wants to write a design theory package, then I really suggest
they consider making use of GRAPE, representing a design via its
incidence graph, and naming the vertices appropriately. For example, a
design record could contain a component "incidenceGraph", on which
GRAPE functions could be applied.

I have been using GRAPE recently to study partial linear spaces with
parameters (s,t). These are 1-(v,s+1,t+1) designs, such that any pair
of distinct blocks meet in at most 1 point.

Hope you find this useful.

Regards, Leonard.

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