Uniformly resolvable decompositions of $K_v$ into $P_3$ and $K_3$ graphs
In this paper we consider the uniformly resolvable decompositions of the complete graph KvKv, or the complete graph minus a 1-factor as appropriate, into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the case in which all the resolution classes consist of either P3P3s or K3K3s.
We consider families of operators satisfying a general class of relations, whose solutions can be described in terms of orbits of some dynamical system acting on the spectrum of a commuting sub-family. In the first section we introduce a class of relations and show, how the representations of such relations are related to orbits of the corresponding dynamical system. Also, we discuss the problem of accurate sense of the relation for unbounded operators. In Section 2, we study the class of *-algebras allowing Wick ordering whose representations can be studied by using methods of Section 1. We classify such Wick *-algebras, and discuss their representations.