Geodesic
Reciprocal domains and {C}ohen-{M}acaulay {\(d\)}-complexes in {\(\mathbb R^ d\)}
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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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 ${\Bbb R}^d$ is necessarily a $d$-ball. This is observed to be true for $d \leq 3$, but false for $d=4$.
DOI : 10.37236/1888
Classification : 52B20, 13H10, 05E99, 57Q05, 51M20
Mots-clés : reciprocal domains, Cohen-Macaulay complex, polyhedral rational cone, lattice point enumerators 
@article{10_37236_1888,
     author = {Ezra Miller and Victor Reiner},
     title = {Reciprocal domains and {{C}ohen-{M}acaulay} {\(d\)}-complexes in {\(\mathbb {R^} d\)}},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1888},
     zbl = {1084.52515},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1888/}
}
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Ezra Miller; Victor Reiner. Reciprocal domains and {C}ohen-{M}acaulay {\(d\)}-complexes in {\(\mathbb R^ d\)}. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1888

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