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Combinatorial proofs of some Bell number formulas

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.

preprint2014arXivOpen access
Mark Shattuck
math.CO
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Mark Shattuck

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