Congruences on the Bell polynomials and the derangement polynomials
Copyright policy )Congruences on the Bell polynomials and the derangement polynomials
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.
6 pages
- Dalian Maritime University China (People's Republic of)
Bell polynomials, Mathematics - Number Theory, Exact enumeration problems, generating functions, congruences, umbral calculus, Stirling numbers, Partitions of sets, Primary 11B75, Secondary 05A15, 05A18, 11A07, Other combinatorial number theory, FOS: Mathematics, Mathematics - Combinatorics, Umbral calculus, Congruences; primitive roots; residue systems, Combinatorics (math.CO), Number Theory (math.NT), derangement polynomials
Bell polynomials, Mathematics - Number Theory, Exact enumeration problems, generating functions, congruences, umbral calculus, Stirling numbers, Partitions of sets, Primary 11B75, Secondary 05A15, 05A18, 11A07, Other combinatorial number theory, FOS: Mathematics, Mathematics - Combinatorics, Umbral calculus, Congruences; primitive roots; residue systems, Combinatorics (math.CO), Number Theory (math.NT), derangement polynomials
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!