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A Steiner 2-design with an automorphism fixing exactly r + 2 points

✍ Scribed by Charles J. Colbourn

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 159 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:5<375::aid-jcd6>3.0.co;2-k

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✦ Synopsis

Doyen conjectured that there is no Steiner 2-design having an automorphism with more than r + 1 but fewer than r + √ r -1 fixed points, where r is the replication number. The falsity of this conjecture is shown by describing 2-(45, 5, 1) designs having an automorphism of order 2 with exactly 13 fixed points.