### Abstract

A triple system of order v and index λ is faithfully enclosed in a triple system of order w ≥ v and index µ ≥ λ when the triples induced on some v elements of the triple system of order w are precisely those from the triple system of order v. When λ = µ, faithful enclosing is embedding; when λ = 0, faithful enclosing asks for an independent set of size v in a triple system of order w. A generalization of Stern’s theorem for embedding is proved: A triple system of order v and index λ can be faithfully enclosed in a triple system of order w and index µ whenever w ≥ 2v + 1, µ ≥ λ and µ = 0 mod gcd(w - 2, 6).

Original language | English (US) |
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Title of host publication | Graphs, Matrices, and Designs |

Publisher | CRC Press |

Pages | 31-42 |

Number of pages | 12 |

ISBN (Electronic) | 0824787900, 9781351444385 |

ISBN (Print) | 9781138403987 |

DOIs | |

State | Published - Jan 1 2017 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Graphs, Matrices, and Designs*(pp. 31-42). CRC Press. https://doi.org/10.1201/9780203719916

**Faithful enclosing of triple systems : A generalization of stern’s theorem.** / Bigelow, David C.; Colbourn, Charles.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Graphs, Matrices, and Designs.*CRC Press, pp. 31-42. https://doi.org/10.1201/9780203719916

}

TY - CHAP

T1 - Faithful enclosing of triple systems

T2 - A generalization of stern’s theorem

AU - Bigelow, David C.

AU - Colbourn, Charles

PY - 2017/1/1

Y1 - 2017/1/1

N2 - A triple system of order v and index λ is faithfully enclosed in a triple system of order w ≥ v and index µ ≥ λ when the triples induced on some v elements of the triple system of order w are precisely those from the triple system of order v. When λ = µ, faithful enclosing is embedding; when λ = 0, faithful enclosing asks for an independent set of size v in a triple system of order w. A generalization of Stern’s theorem for embedding is proved: A triple system of order v and index λ can be faithfully enclosed in a triple system of order w and index µ whenever w ≥ 2v + 1, µ ≥ λ and µ = 0 mod gcd(w - 2, 6).

AB - A triple system of order v and index λ is faithfully enclosed in a triple system of order w ≥ v and index µ ≥ λ when the triples induced on some v elements of the triple system of order w are precisely those from the triple system of order v. When λ = µ, faithful enclosing is embedding; when λ = 0, faithful enclosing asks for an independent set of size v in a triple system of order w. A generalization of Stern’s theorem for embedding is proved: A triple system of order v and index λ can be faithfully enclosed in a triple system of order w and index µ whenever w ≥ 2v + 1, µ ≥ λ and µ = 0 mod gcd(w - 2, 6).

UR - http://www.scopus.com/inward/record.url?scp=85063548296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063548296&partnerID=8YFLogxK

U2 - 10.1201/9780203719916

DO - 10.1201/9780203719916

M3 - Chapter

SN - 9781138403987

SP - 31

EP - 42

BT - Graphs, Matrices, and Designs

PB - CRC Press

ER -