A survey of Kirkman triple systems and related designs

DOI10.1016/0012-365X(91)90294-CzbMath0751.05012OpenAlexW2071389349MaRDI QIDQ1182956

Douglas R. Stinson

Publication date: 28 June 1992

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(91)90294-c

zbMATH Keywords

Steiner triple systemKirkman triple system

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Triple systems (05B07)

Related Items (21)

New results on LR-designs and OLKTSs ⋮ A construction for large sets of disjoint Kirkman triple systems ⋮ Ramsey-nice families of graphs ⋮ On the existence of (3,λ)-semiframes of type 3^u ⋮ The intersection numbers of nearly Kirkman triple systems ⋮ On colorful edge triples in edge-colored complete graphs ⋮ Some new Kirkman signal sets ⋮ The 3-way intersection problem for Kirkman triple systems ⋮ Generalized packing designs ⋮ Constructions for large sets of \(v-1\{0,{v\over 3}\}\)-intersecting Steiner triple systems of order \(v\) ⋮ Existence of frame-derived H-designs ⋮ A new result on Sylvester's problem ⋮ Scheduling to reduce close contacts: resolvable grid graph decomposition and packing ⋮ On the seven non-isomorphic solutions of the fifteen schoolgirl problem ⋮ The intersection numbers of KTSs with a common parallel class ⋮ On large sets of Kirkman triple systems and 3-wise balanced design. ⋮ Further results on large sets of Kirkman triple systems ⋮ Large sets of Kirkman triple systems of orders \(2^{2 n + 1} + 1\) ⋮ Intersection numbers of Kirkman triple systems ⋮ Constructions and uses of incomplete pairwise balanced designs ⋮ The flower intersection problem for Kirkman triple systems

Cites Work

• Existence results for doubly near resolvable \((v,3,2)\)-BIBDs
• Resolvable group divisible designs with block size 3
• On combinatorial designs with subdesigns
• A Kirkman square of order 51 and block size 3
• Orthogonal packings in PG(5,2)
• Frames for Kirkman triple systems
• Pairwise balanced designs with block sizes \(6t+1\)
• On the existence of frames
• On projective planes of order 12 with an automorphism of order 13. I: Kirkman designs of order 27
• On resolvable balanced incomplete block designs
• Balanced incomplete block designs and related designs
• Group divisible designs with block-size four
• A doubly divisible nearly Kirkman system
• Further cases of double resolvability
• Double resolvability of some complete 3-designs
• On the (15,5,\(\lambda\) )-family of BIBDs
• Intersections among Steiner systems
• Sylvester's problem of the 15 schoolgirls
• Nonisomorphic Steiner triple systems
• 3-complementary frames and doubly near resolvable (v,3,2)-BIBDs
• Kirkman Cubes
• A Note on the Existence of Strong Kirkman Cubes
• T. P. Kirkman, Mathematician
• A Class of Steiner Triple Systems of Order 21 and Associated Kirkman Systems
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