| author: | Veerle Fack, Svetlana Topalova and Joost Winne |
|---|---|
| title: | On the enumeration of uniquely reducible double designs |
| keywords: | double design, projective plane, enumeration |
| abstract: |
A double 2-(
v
,
k
,
2λ
) design is a design which is reducible into two 2-(
v
,
k
,
λ
) 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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| reference: | Veerle Fack and Svetlana Topalova and Joost Winne (2005), On the enumeration of uniquely reducible double designs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 129-132 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| ps-source: | dmAE0125.ps (127 K) |
| pdf-source: | dmAE0125.pdf (134 K) |
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