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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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