An extension of the Kruskal-Katona theorem to colored hypergraphs was given by Frankl, Füredi and Kalai in [Shadows of colored complexes, Mathematica Scandinavica]. Here we give a new simple proof. © 1994.
London, E. (1994). A new proof of the colored Kruskal-Katona theorem. Discrete Mathematics, 126(1–3), 217–223. https://doi.org/10.1016/0012-365X(94)90266-6