Reciprocal domains and Cohen-Macaulay d-complexes in ℝd

Ezra Miller, Victor S Reiner

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 ℝd is necessarily a d-ball. This is observed to be true for d ≤ 3, but false for d = 4.

Original languageEnglish (US)
Article numberN1
Pages (from-to)1-9
Number of pages9
JournalElectronic Journal of Combinatorics
Issue number2 N
StatePublished - Jan 7 2005


  • Canonical module
  • Cohen-Macaulay
  • Matlis duality
  • Reciprocal domain
  • Reciprocity
  • Semigroup ring


Dive into the research topics of 'Reciprocal domains and Cohen-Macaulay d-complexes in ℝ<sup>d</sup>'. Together they form a unique fingerprint.

Cite this