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For stacked simplicial complexes, (special subclasses of such are: trees,triangulations of polygons, stacked polytopes), we give an explicit bijectionbetween partitions of facets (for trees: edges), and partitions of verticesinto independent sets. More generally we give bijections between facetpartitions whose parts have minimal distance $\geq s$ and vertex partitionswhose parts have minimal distance $\geq s+1$. A consequence is results onpartitions of natural numbers, where the parts have minimal bounds on spacing.

Partitons of vertices and facets in trees and stacked simplicial complexes