In 1996 Manjul Barghava introduced a notion of P-orderings for arbitrary sets S of a Dedekind domain, with respect to a prime ideal P, which defined associated invariants called P-sequences. He combined these invariants to define generalized factorials and binomial coefficients associated to the subset S. These factorials were used in characterizing rings of polynomials that are integer-valued on S. Further generalizations of P-orderings by Bhargava in 2009 (with more parameters) have many applications. This talk defines analogous invariants for all proper ideals B of a Dedekind domain, called B-sequences, and extends the notion of generalized factorials and binomial coefficients to this setting. (This is joint work with Wijit Yangjit (U. Michigan))
This video is part of the Institute for Advanced Study‘s Special year research seminar.
