Some of the S(2,3,n) systems can have their blocks be partitioned into (n-1)/2 sets of (n/3) triples each. This is called "resolvable" and such systems are called "Kirkman triple systems" after Thomas Kirkman, who studied such resolvable systems before Steiner. Dale Mesner, Earl Kramer, and others investigated collections of Steiner triple systems that are mutually disjoint (i.e., no two Steiner systems in such a collection share a common triplet). It is known (Bays 1917, Kramer & Mesner 1974) that seven different S(2,3,9) systems can be generated to together cover all 84 triplets on a 9-set; it was also known by them that there are 15360 different ways to find such 7-sets of solutions, which reduce to two non-isomorphic solutions under relabeling, with multiplicities 6720 and 8640 respectively. The corresponding question for finding thirteen different disjoint S(2,3,15) systems was asked by James Sylvester in 1860 and answered by RHF Denniston in 1974. There is at least one such 13-set of S(2,3,15) but its isomorphism is not known.