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Dear GAP-Forum,

1. Applications to combinatorial topology

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A while ago in the GAP Forum I mentioned that Sarah Rees and I were

working on algorithms to compute fundamental groups, first homology

groups, first homology groups mod p, deck groups, and covers of certain

"combinatorial cell complexes". This work has now appeared in:

S. Rees and L.H. Soicher, An algorithmic approach to fundamental groups

and covers of combinatorial cell complexes, J. Symbolic Comp. 29

(2000), 59-77.

In that paper there is an extended example using GAP3 implementations

of our algorithms for the case of clique complexes. I now have a

preliminary GAP4 implementation, which works in the more general case

of simplicial complexes. If you are interested in these programs I'd be

glad to send you a copy (and any comments would be welcome).

2. Applications to design theory

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On another topic, you may be interested in applications of GAP and GRAPE

to the discovery and classification of certain types of combinatorial

designs, called SOMAs. Here the relevant paper is:

L.H. Soicher, On the structure and classification of SOMAs:

generalizations of mutually orthogonal Latin squares, Electronic J.

Combinatorics 6 (1999), #R32, 15 pp.

which is available at:

http://www.combinatorics.org/Volume_6/Abstracts/v6i1r32.html

More recent discoveries in this area appear at

http://www.maths.qmw.ac.uk/~leonard/soma/

Hope this is of interest, Leonard.

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