Article ID Journal Published Year Pages File Type
9492796 Expositiones Mathematicae 2005 9 Pages PDF
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 τp, the relation Bn=-Tr(ϑn-1-τp)Bτp holds in Fp, where ϑ is a root of g˜(x)=xp-x-1 and Tr:Fp[ϑ]⟶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].
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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