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Symmetric (41,16,6)-designs with a nontrivial automorphism of odd order

✍ Scribed by Edward Spence

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 722 KB
Volume: 1
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180010303

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✦ Synopsis

Abstract

If a symmetric (41,16,6)‐design has an automorphism σ of odd prime order q then q = 3 or 5. In the case q = 5 we determine all such designs and find a total of 419 nonisomorphic ones, of which 15 are self‐dual. When q = 3 a combinatorial explosion occurs and the complete classification becomes impracticable. However, we give a characterization in the particular case when σ has order 3 and fixes 11 points, and find that there are 3,076 nonisomorphic designs with this property, all of them being non self‐dual. The other remaining possibility is that σ, of order 3, fixes 5 points. In this case there are 960 orbit matrices (up to isomorphism and duality) and all but one of them yield designs. Here an incomplete investigation shows that in total there are at least 112,000 nonisomorphic designs. © 1993 John Wiley & Sons, Inc.

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