Set-coloring a graph means giving each vertex a subset of a fixed color set so that no two adjacent subsets have the same cardinality. When the graph is complete one gets a new distribution problem with an interesting generating function. We explore examples and generalizations.
@article{arxiv.math/0609049,
title = {A new distribution problem of balls into urns, and how to color a graph by different-sized sets},
author = {Thomas Zaslavsky},
journal= {arXiv preprint arXiv:math/0609049},
year = {2007}
}