If you've been struggling with the ancient problem of Josephus, you're in luck. Cal State East Bay Professor of Mathematics & Computer Science Christopher Morgan will soon publish his latest research on this topic.
Morgan's article, "An application of Fourier transforms on finite Abelian groups to an enumeration arising from the Josephus problem," appears in the April 2010 issue of the Journal of Number Theory. He and Gregory L. Wilson, BerrieHill Research Corporation, analyze an enumeration associated with the Josephus problem by applying a Fourier transform to a multivariate generating function. This yields a formula for the enumeration that reduces to a simple expression under a condition called local prime abundance. A resulting computation shows that the enumeration is nontrivial for this case.
Lost?! A video is posted to youtube.com to help explain.
CSUEB staff, students, and faculty have full access to this article via ScienceDirect (PDF).