Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9492796 | Expositiones Mathematicae | 2005 | 9 Pages |
Abstract
The nth Bell number Bn is the number of ways to partition a set of n elements into nonempty subsets. We generalize the “trace formula” of Barsky and Benzaghou [1], which asserts that for an odd prime p and an appropriate constant Ïp, the relation Bn=-Tr(Ïn-1-Ïp)BÏp holds in Fp, where Ï is a root of gË(x)=xp-x-1 and Tr:Fp[Ï]â¶Fp is the trace form. We deduce some new interesting congruences for the Bell numbers, generalizing miscellaneous well-known results including those of Radoux [4].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alexandre Junod,