A conjecture on small embeddings of partial Steiner triple systems | Zendy

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A conjecture on small embeddings of partial Steiner triple systems

Author(s) -

Bryant Darryn

Publication year - 2002

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.10017

Subject(s) - conjecture , order (exchange) , steiner system , combinatorics , mathematics , discrete mathematics , economics , finance

A well‐known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order υ for all υ ≡ 1 or 3, (mod 6), υ ≥ 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order υ <2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 313–321, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10017

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