Combinatorial proofs of some Bell number formulas

zbMATH Open1337.05011arXiv1401.6588MaRDI QIDQ2809933

Mark Shattuck

Publication date: 30 May 2016

Published in: JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1401.6588

zbMATH Keywords

complete Bell polynomialsbijective proofs of identities

Mathematics Subject Classification ID

Partitions of sets (05A18) Bell and Stirling numbers (11B73)

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