Stirling complexes

Abstract In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number resources labeled nodes tree network, so that no node is left empty. These turn out be cubical complexes, which can thought as higher-dimensional geometric extensions combinatorial Stirling partitioning set named objects into non-empty parts. As our main result, prove these complexes are always homotopy equivalent wedges spheres same dimension. Furthermore, provide several formulae count spheresSomewhat surprisingly, type turns depend only on and nodes, not actual structure network.