Further results on overlarge sets of Kirkman triple systems
An overlarge set of Steiner triple systems on \(v\) vertices, \(\text{OLSTS}(v)\), is a collection \(\{(X-x,\mathcal{B}_{x}),x\in X,\left| X\right| =v+1\}\) of \(v+1\) Steiner triple systems on \(v\) vertices, \(\text{STS}(v),\) where \(\{\mathcal{ B}_{x},x\in X\}\) constitutes a partition of all triples on \(X.\) The spectrum of \(\text{OLSTS}(v)\) has been completely determined by M. J. Sharry and A. P. Street. If we substitute \(STS(v)\) by the Kirkman triple system then we get the notion of the overlarge set of Kirkman triple systems, \(\text{OLKTS}(v).\) The spectrum of \(\text{OLKTS}(v)\) is not known yet. In the paper the authors provide new constructions of \(\text{OLKTS}(v)\) for some specific values of \(v.\)
scientific article; zbMATH DE number 5629510