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

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)375-380
Number of pages6
JournalJournal of Combinatorial Designs
Volume7
Issue number5
DOIs
StatePublished - Jan 1 1999
Externally publishedYes

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Keywords

  • Block design
  • Steiner 2-design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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