# On the enumeration of uniquely reducible double designs

Abstract : A double $2$-$(v,k,2 \lambda)$ design is a design which is reducible into two $2$-$(v,k,\lambda)$ designs. It is called uniquely reducible if it has, up to equivalence, only one reduction. We present properties of uniquely reducible double designs which show that their total number can be determined if only the designs with non-trivial automorphisms are classified with respect to their automorphism group. As an application, after proving that a reducible $2$-$(21,5,2)$ design is uniquely reducible, we establish that the number of all reducible $2$-$(21,5,2)$ designs is $1 746 461 307$.
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Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.129-132, 2005, DMTCS Proceedings
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https://hal.inria.fr/hal-01184373
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Soumis le : vendredi 14 août 2015 - 11:38:09
Dernière modification le : jeudi 11 mai 2017 - 01:02:53
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• HAL Id : hal-01184373, version 1

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Veerle Fack, Svetlana Topalova, Joost Winne. On the enumeration of uniquely reducible double designs. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.129-132, 2005, DMTCS Proceedings. 〈hal-01184373〉

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