%0 Journal Article
%T Reciprocal domains and Cohen-Macaulay $d$-complexes in $R^d$
%A Ezra Miller
%A Victor Reiner
%J Mathematics
%D 2004
%I arXiv
%X We extend a reciprocity theorem of Stanley about enumeration of integer points in polyhedral cones when one exchanges strict and weak inequalities. The proof highlights the roles played by Cohen-Macaulayness and canonical modules. The extension raises the issue of whether a Cohen-Macaulay complex of dimension d embedded piecewise-linearly in d-space is necessarily a d-ball. This is observed to be true for d at most 3, but false for d=4.
%U http://arxiv.org/abs/math/0408169v1