Simple signed Steiner triple systems

2011/05/14 by Ebrahim Ghorbani, E. Ghorbani, Ghorbani, E. +2
Engineering · Mathematics · #05B05 #05B07 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #msc:05B05 #msc:05B07

paper · pdf · doi:10.48550/arxiv.1105.2896

11 pages, 1 table. Final version. To appear in Journal of Combinatorial Designs

openalex publication_date 2011/05/14 · arxiv created 2011/11/13 · arxiv updated 2011/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a v-set, \B a set of 3-subsets (triples) of X, and \B⁺∪\B^- a partition of \B with |\B^-|=s. The pair (X,\B) is called a simple signed Steiner triple system, denoted by ST(v,s), if the number of occurrences of every 2-subset of X in triples B∈\B⁺ is one more than the number of occurrences in triples B∈\B^-. In this paper we prove that \st(v,s) exists if and only if v≡1,3\pmod6, v≠7, and s∈\0,1,...,s_v-6,s_v-4,s_v\, where s_v=v(v-1)(v-3)/12 and for v=7, s∈\0,2,3,5,6,8,14\.

Related

• On determining when small embeddings of partial Steiner triple systems\n exist
• Threshold for Steiner triple systems
• Cancellative hypergraphs and Steiner triple systems
• Duplicated Steiner triple systems with self-orthogonal near resolutions
• On a conjecture of Erdős on locally sparse Steiner triple systems