Generalization of Stanley's monster reciprocity theorem

By studying the reciprocity property of linear Diophantine systems in light of Malcev-Neumann series, we present in this paper a new approach to and a generalization of Stanley’s monster reciprocity theorem. A formula for the “error term” is given in the case when the system does not have the reciprocity property. We also give a short proof of Stanley’s reciprocity theorem for linear homogeneous Diophantine systems.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Guoce Xin
• Keywords: Diophantine Systems, JCT 2007, Reciprocity Property, Stanley’s Monster Reciprocity