# 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 $1 746 461 307$.
Keywords :
Document type :
Conference papers
Domain :
Complete list of metadata

Cited literature [6 references]

https://hal.inria.fr/hal-01184373
Contributor : Coordination Episciences Iam <>
Submitted on : Friday, August 14, 2015 - 11:38:09 AM
Last modification on : Friday, September 6, 2019 - 11:14:03 AM
Long-term archiving on: : Sunday, November 15, 2015 - 11:03:08 AM

### File

dmAE0125.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01184373, version 1

### Citation

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. ⟨hal-01184373⟩

Record views