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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

On the enumeration of uniquely reducible double designs

Résumé

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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Dates et versions

hal-01184373 , version 1 (14-08-2015)

Identifiants

Citer

Veerle Fack, Svetlana Topalova, Joost Winne. On the enumeration of uniquely reducible double designs. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.129-132, ⟨10.46298/dmtcs.3416⟩. ⟨hal-01184373⟩

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