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

Charles J. Colbourn

doi:10.1002/(SICI)1520-6610(1999)7:5

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

Charles J. Colbourn

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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 language	English (US)
Pages (from-to)	375-380
Number of pages	6
Journal	Journal of Combinatorial Designs
Volume	7
Issue number	5
DOIs	https://doi.org/10.1002/(SICI)1520-6610(1999)7:5
State	Published - Jan 1 1999
Externally published	Yes

Keywords

Block design
Steiner 2-design

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1002/(SICI)1520-6610(1999)7:5

Cite this

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title = "A Steiner 2-design with an automorphism fixing exactly r + 2 points",

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.",

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AU - Colbourn, Charles J.

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N2 - 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.

AB - 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.

KW - Block design

KW - Steiner 2-design

UR - https://www.scopus.com/pages/publications/27844472156

UR - https://www.scopus.com/pages/publications/27844472156#tab=citedBy

U2 - 10.1002/(SICI)1520-6610(1999)7:5

DO - 10.1002/(SICI)1520-6610(1999)7:5

M3 - Article

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VL - 7

SP - 375

EP - 380

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 5

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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