Kirkman triple systems of order 21 with nontrivial automorphism group

Myra B. Cohen; Charles J. Colbourn; Lee A. Ives; Alan C.H. Ling

doi:10.1090/S0025-5718-01-01372-2

Kirkman triple systems of order 21 with nontrivial automorphism group

Myra B. Cohen, Charles J. Colbourn, Lee A. Ives, Alan C.H. Ling

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

9 Scopus citations

Abstract

There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).

Original language	English (US)
Pages (from-to)	873-881
Number of pages	9
Journal	Mathematics of Computation
Volume	71
Issue number	238
DOIs	https://doi.org/10.1090/S0025-5718-01-01372-2
State	Published - Jan 1 2002
Externally published	Yes

Keywords

Constructive enumeration
Doubly resolvable design
Kirkman triple system
Steiner triple system

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-01-01372-2

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abstract = "There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).",

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T1 - Kirkman triple systems of order 21 with nontrivial automorphism group

AU - Cohen, Myra B.

AU - Colbourn, Charles J.

AU - Ives, Lee A.

AU - Ling, Alan C.H.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).

AB - There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).

KW - Constructive enumeration

KW - Doubly resolvable design

KW - Kirkman triple system

KW - Steiner triple system

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Kirkman triple systems of order 21 with nontrivial automorphism group

Abstract

Keywords

ASJC Scopus subject areas

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