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A Steiner 2‐design with an automorphism fixing exactly r + 2 points
Author(s) -
Colbourn Charles J.
Publication year - 1999
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1999)7:5<375::aid-jcd6>3.0.co;2-k
Subject(s) - mathematics , steiner system , combinatorics , automorphism , conjecture , order (exchange) , falsity , automorphism group , discrete mathematics , linguistics , philosophy , finance , economics
Doyen conjectured that there is no Steiner 2‐design having an automorphism with more than r + 1 but fewer than $r + \sqrt{r - 1}$ 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. © 1999 John Wiley & Sons, Inc. J Combin Design 7: 375–380, 1999