Generalization of Stanley's monster reciprocity theorem

  • Authors:

  • Guoce Xin

  • Affiliations:

  • Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2007

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Abstract

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 an inductive proof of Stanley's reciprocity theorem for linear homogeneous Diophantine systems.