Reciprocal domains and Cohen-Macaulay $d$-complexes in $R^d$

Details Reciprocal domains and Cohen-Macaulay $d$-complexes in $R^d$ Reciprocal domains and Cohen-Macaulay $d$-complexes in $R^d$

2004-08-12

arxiv.org/abs/math/0408169v1

Mathematics

Combinatorics

Scientific paper

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.

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