Congruences on the Bell polynomials and the derangement polynomials

2010/09/15 by Yidong Sun, Sun, Yidong, Xiaojuan Wu +3
Mathematics · #05A18 #11A07 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11B75 #Secondary 05A15 #math.CO #math.NT #msc:05A15 #msc:05A18 #msc:11A07 #msc:11B75

paper · pdf · doi:10.48550/arxiv.1009.2929

6 pages

arxiv created 2010/09/15 · arxiv updated 2010/09/16

Abstract

In this note, by the umbra calculus method, the Sun and Zagier's congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences are also provided.

Related

• A remarkable congruence involving Appell polynomials
• On a curious property of Bell numbers
• Some identities of degeenrate ordered Bell polynomials and numbers arising from umbral calculus
• A note on degenerate Bell numbers and polynomials
• A new extension of the Sun-Zagier result involving Bell numbers and derangement numbers