Binomial partial Steiner triple systems with complete graphs: structural problems

TL;DR

This paper investigates the structural properties of hyperplanes within binomial partial Steiner triple systems, which are configurations characterized by specific point and line counts, focusing on their geometric and combinatorial features.

Contribution

It provides a detailed analysis of the hyperplanes in BSTS, revealing new structural insights into these combinatorial configurations.

Findings

Characterization of hyperplanes in BSTS

Identification of structural constraints of BSTS hyperplanes

Insights into the combinatorial geometry of Steiner systems

Abstract

In the paper we study the structure of hyperplanes of so called binomial partial Steiner triple systems (BSTS's, in short) i.e. of configurations with $\binom{n}{2}$ points and $\binom{n}{3}$ lines, each line of the size $3$. Consequently, a BSTS has $n-2$ lines through each of its points.