On the indecomposable partition problem: IPP(10, \(\Lambda\)) (Q1598830)

The indecomposable partition problem, \(\text{IPP}(v,\Lambda)\), posed by \textit{C. J. Colbourn} and \textit{J. J. Harms} [Partitions into indecomposable triple systems, Ann. Discrete Math. 34, 107-118 (1987; Zbl 0646.05007)] is as follows: Let \(\Lambda= \lambda_1+\cdots+ \lambda_s\), \(\lambda_1\leq \lambda_2\leq\cdots\leq \lambda_s\), be a partition of \(v-2\) and let \(X\) be a set of \(v\) letters. Now the question is if it is possible to partition the blocks of the complete triple system of \(v\) points into \(s\) classes \(B_1,\dots, B_s\) so that \((X,B_i)\) is an indecomposable triple system \(\text{TS}(v,\lambda_i)\) for all \(i\) with \(1\leq i\leq s\). We recall that a triple system is called indecomposable if there is no proper nonempty subset \(B'\) of \(B\) for which \((X,B')\) is a triple system. In the paper cited above Colbourn and Harms showed that an \(\text{IP}(10,\Lambda)\) exists if and only if \(\Lambda\equiv 2+2+2+2\), \(2+2+4\) or \(4+4\). The aim of the note under review is to determine all nonrigid indecomposable \(\text{TS}(10,4)\) and to find the exact number of \(\text{IP}(10,\Lambda)\) where \(\Lambda\equiv 4+4\). Most of the note consists of numerical tables and known results from previous papers. No proofs are given for the statements mentioned in the note and there is no way one can be sure of the numbers given in the statements of the results.