Reciprocal domains and Cohen-Macaulay d-complexes in ℝd


Journal Article

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.

Duke Authors

Cited Authors

  • Miller, E; Reiner, V

Published Date

  • January 7, 2005

Published In

Volume / Issue

  • 11 / 2 N

Start / End Page

  • 1 - 9

Electronic International Standard Serial Number (EISSN)

  • 1077-8926

International Standard Serial Number (ISSN)

  • 1077-8926

Citation Source

  • Scopus