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Some Constructions of Steiner Triple Systems of Type v⟶2v + 1 + 6k | Synapse

March 5, 2026Open Access

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Some Constructions of Steiner Triple Systems of Type v⟶2v + 1 + 6k

LFL. FragapaneUniversity of Catania MGMario GionfriddoUniversity of Catania

Key Points

To explore new constructions of Steiner Triple Systems (STS) of specific types and order.
Analyzed the properties of Steiner Triple Systems of order v.
Investigated constructions of STS(v) for types v≥v+20 and v≥v+40.
Examined all possible cases of formations within the defined parameters.
Identified unique structures within the larger category of Steiner Triple Systems.
Demonstrated that both STS types can be constructed under the given conditions.

Abstract

A Steiner Triple System (STS) of order v is a hypergraph Σ=(X,B) that is uniform of rank 3 and has order v, such that every 2-subset of X has degree 1. In this paper, we present some constructions of STS(v) of type v⟶v+20 and v⟶v+40, examining all possible cases.

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Cite This Study

Fragapane et al. (Mon,) studied this question.

synapsesocial.com/papers/69a91d55d6127c7a504c01a9 https://doi.org/https://doi.org/10.3390/math14050850