Combinatorial proofs of some Bell number formulas
arXiv:1401.6588
Abstract
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further interpretation for a related difference of Catalan numbers in terms of the inclusion-exclusion principle.
Paper accepted at the Journal of Combinatorial Mathematics and Combinatorial Computing and is to appear in an upcoming issue