Doubly resolvable nearly Kirkman triple systems

R. Julian R Abel; Nigel Chan; Charles Colbourn; E. R. Lamken; Chengmin Wang; Jinhua Wang

doi:10.1002/jcd.21342

Doubly resolvable nearly Kirkman triple systems

R. Julian R Abel, Nigel Chan, Charles Colbourn, E. R. Lamken, Chengmin Wang, Jinhua Wang

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15 Scopus citations

Abstract

Necessary conditions for existence of a resolvable group divisible design (GDD) with block size 3 and type 2v/2 (a nearly Kirkman triple system, NKTS(v)), are v≥18 and v≡0 (mod 6). In this paper, we look at doubly resolvable NKTS(v)s; here we find that these necessary conditions are sufficient, except possibly for 64 values of v.

Original language	English (US)
Pages (from-to)	342-358
Number of pages	17
Journal	Journal of Combinatorial Designs
Volume	21
Issue number	8
DOIs	https://doi.org/10.1002/jcd.21342
State	Published - Aug 2013

Keywords

Kirkman square
doubly resolvable
frame AMS subject classification: 05B07
nearly Kirkman triple system

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1002/jcd.21342

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abstract = "Necessary conditions for existence of a resolvable group divisible design (GDD) with block size 3 and type 2v/2 (a nearly Kirkman triple system, NKTS(v)), are v≥18 and v≡0 (mod 6). In this paper, we look at doubly resolvable NKTS(v)s; here we find that these necessary conditions are sufficient, except possibly for 64 values of v.",

keywords = "Kirkman square, doubly resolvable, frame AMS subject classification: 05B07, nearly Kirkman triple system",

author = "Abel, {R. Julian R} and Nigel Chan and Charles Colbourn and Lamken, {E. R.} and Chengmin Wang and Jinhua Wang",

year = "2013",

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T1 - Doubly resolvable nearly Kirkman triple systems

AU - Abel, R. Julian R

AU - Chan, Nigel

AU - Colbourn, Charles

AU - Lamken, E. R.

AU - Wang, Chengmin

AU - Wang, Jinhua

PY - 2013/8

Y1 - 2013/8

N2 - Necessary conditions for existence of a resolvable group divisible design (GDD) with block size 3 and type 2v/2 (a nearly Kirkman triple system, NKTS(v)), are v≥18 and v≡0 (mod 6). In this paper, we look at doubly resolvable NKTS(v)s; here we find that these necessary conditions are sufficient, except possibly for 64 values of v.

AB - Necessary conditions for existence of a resolvable group divisible design (GDD) with block size 3 and type 2v/2 (a nearly Kirkman triple system, NKTS(v)), are v≥18 and v≡0 (mod 6). In this paper, we look at doubly resolvable NKTS(v)s; here we find that these necessary conditions are sufficient, except possibly for 64 values of v.

KW - Kirkman square

KW - doubly resolvable

KW - frame AMS subject classification: 05B07

KW - nearly Kirkman triple system

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JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 8

ER -

Doubly resolvable nearly Kirkman triple systems

Abstract

Keywords

ASJC Scopus subject areas

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