Congruences on the Bell polynomials and the derangement polynomials

DOI10.1016/j.jnt.2012.08.031zbMath1339.11035arXiv1009.2929OpenAlexW2964197522MaRDI QIDQ1937303

Yidong Sun, Jujuan Zhuang, Xiao-Juan Wu

Publication date: 28 February 2013

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2929

zbMATH Keywords

congruencesStirling numbersumbral calculusBell polynomialsderangement polynomials

Mathematics Subject Classification ID

Umbral calculus (05A40) Exact enumeration problems, generating functions (05A15) Partitions of sets (05A18) Other combinatorial number theory (11B75) Congruences; primitive roots; residue systems (11A07)

Related Items (6)

Backward Touchard congruence ⋮ Set partitions and partitions without singleton blocks of type \(B\) ⋮ Identities behind some congruences for \(r\)-Bell and derangement polynomials ⋮ Curious congruences related to the Bell polynomials ⋮ Divisibility properties of the \(r\)-Bell numbers and polynomials ⋮ Derangements and the 𝑝-adic incomplete gamma function

Cites Work

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• \(\lambda \)-factorials of \(n\)
• The largest singletons of set partitions
• Enumeration of derangements with descents in prescribed positions
• A generalized recurrence for Bell polynomials: an alternate approach to Spivey and Gould-Quaintance formulas
• The umbral calculus
• Catalan, Motzkin, and Riordan numbers
• Some congruences concerning the Bell numbers
• Applications of the classical umbral calculus
• ON A CURIOUS PROPERTY OF BELL NUMBERS

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