Combinatorial proofs of some Bell number formulas

2014/01/25 by Mark Shattuck, Shattuck, Mark
Engineering · Mathematics · #05A18 #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05A18 #msc:05A19

paper · pdf · doi:10.48550/arxiv.1401.6588

Paper accepted at the Journal of Combinatorial Mathematics and Combinatorial Computing and is to appear in an upcoming issue

arxiv created 2014/01/25 · openalex publication_date 2014/01/25 · arxiv updated 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The r-Bell numbers
• The role of binomial type sequences in determination identities for Bell polynomials
• On poly-Bell numbers and polynomials
• Partial Deranged Bell Numbers and Their Combinatorial Properties
• A new approach to Bell and poly-Bell numbers and polynomials