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Good evening, I am currently taking a class which has combinatorial designs as the first topic, we are using Peter Cameron's book Designs, Graphs, Codes and their Links which I am finding extremely interesting. I am really interested in a rigorous study of combinatorial designs without their links now.Of course I plan to continue taking the class, but I would really like to read a textbook just on designs (I am especially interested in realizable designs (like the social golfer and Kirkman girl problem)).

Thank you very much in advance.

Regards.

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There is a list of references in http://www.maths.qmul.ac.uk/~pjc/design/resources.html#books and http://en.wikipedia.org/wiki/Block_design#References

From the latter, I know books by Beth et al (a long and detailed) and by Hughes and Piper (shorter and more readable).

All of it is outdated in several important aspects, e.g. the huge progress on existence questions made by P.Keevash in http://arxiv.org/abs/1401.3665 is understandably not there.

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You could try "Stinson - Combinatorial design theory" too. Also, just in case it might interest you: I am half-learning design theory myself and trying to implement the constructive proof of existence that I find in the software Sage.

The goal is to be able to actually build all the combinatorial designs which exist in the litterature. I'd be delighted to not be alone in the attempt.

You can see what is already implemented on This page

Also, you will find pointers from our implemented constructions to the paper/books that provide the instructions, so that this also partly answers your question.

Finally, you may want to find a copy of the "Handbook of Combinatorial Designs" somewhere. It is not a textbook at all, but there is just no way to know what exists and what does not without this ;-)

Good luck !

Nathann

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