Face numbers of generalized balanced Cohen-Macaulay complexes

Abstract

A common generalization of two theorems on the face numbers of Cohen-Macaulay (CM, for short) simplicial complexes is established: the first is the theorem of Stanley (necessity) and Björner-Frankl-Stanley (sufficiency) that characterizes all possible face numbers of a-balanced CM complexes, while the second is the theorem of Novik (necessity) and Browder (sufficiency) that characterizes the face numbers of CM subcomplexes of the join of the boundaries of simplices.

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Correspondence to Jonathan Browder.

Additional information

Novik’s research is partially supported by Alfred P. Sloan Research Fellowship and NSF grant DMS-0801152

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Browder, J., Novik, I. Face numbers of generalized balanced Cohen-Macaulay complexes. Combinatorica 31, 669–689 (2011). https://doi.org/10.1007/s00493-011-2675-7

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Mathematics Subject Classification (2000)

  • 05E45
  • 52B22
  • 13F55