Stirling complexes (Q6102902)

In this paper the author introduces the so called \textit{Stirling complexes}, which can be viewed as ``natural reconfiguration spaces associated to the problem of distributing a fixed number of resources to labeled nodes of a tree network, so that no node is left empty.'' He proves that such spaces are ``cubical complexes, which can be thought of as higher-dimensional geometric extensions of the combinatorial Stirling problem of partitioning a set of named objects into non-empty labeled parts'' (hence their name). The main result, namely Theorem 2.1, is that ``Stirling complexes are always homotopy equivalent to wedges of spheres of the same dimension.'' Furthermore, the author provides several ``combinatorial formulae to count these spheres.'' Moreover, he obtains the following (somewhat surprising) result that ``the homotopy type of the Stirling complexes depends only on the number of resources and the number of the labeled nodes, not on the actual structure of the tree network.''