A Generalization of Stanley's Monster Reciprocity Theorem

Details A Generalization of Stanley's Monster Reciprocity Theorem A Generalization of Stanley's Monster Reciprocity Theorem

2005-04-21

arxiv.org/abs/math/0504425v1

Mathematics

Combinatorics

22 pages, 1 figures

Scientific paper

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.

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