Shifting powers in Spivey’s Bell number formula

DOI10.2989/16073606.2020.1848936zbMath1492.05013OpenAlexW3112165859MaRDI QIDQ5065552

Toufik Mansour, Reza Rastegar, Mark Shattuck, Alexander Roitershtein

Publication date: 22 March 2022

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2020.1848936

zbMATH Keywords

Bell numbercombinatorial identityWhitney numberSpivey's formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19)

Related Items (1)

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• Closed expressions for averages of set partition statistics
• Extensions of Spivey's Bell number formula
• \(r\)-Whitney numbers of Dowling lattices
• A generalization of the \(r\)-Whitney numbers of the second kind
• A new formula for the Bernoulli polynomials
• A unified approach to some recurrence sequences via Faà di Bruno's formula
• The \(r\)-Stirling numbers
• A generalized recurrence for Bell polynomials: an alternate approach to Spivey and Gould-Quaintance formulas
• On Whitney numbers of Dowling lattices
• A unified approach to generalized Stirling numbers
• On some numbers related to Whitney numbers of Dowling lattices
• The \(r\)-Dowling-Lah polynomials
• A new approach to the \(r\)-Whitney numbers by using combinatorial differential calculus
• The \(r\)-Lah numbers
• A combinatorial approach to a general two-term recurrence
• The $r$-Bell numbers
• Rook theoretic proofs of some identities related to Spivey's Bell number formula
• Spivey's Bell Number Formula Revisited
• Sums of r-Lah numbers and r-Lah polynomials
• Some formulas for Bell numbers
• Finite Automata, Probabilistic Method, and Occurrence Enumeration of a Pattern in Words and Permutations
• Generalizations of Bell number formulas of spivey and Mező
• Some identities related to ther-Whitney numbers

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