Face numbers of generalized balanced Cohen-Macaulay complexes

TL;DR

This paper generalizes key theorems on face numbers of Cohen-Macaulay complexes, providing a unified characterization for a broader class of balanced complexes and their subcomplexes.

Contribution

It establishes a common generalization of two major theorems, extending face number characterizations to generalized balanced Cohen-Macaulay complexes.

Findings

Unified face number characterization for generalized balanced CM complexes

Extension of Stanley and Bjorner-Frankl-Stanley's theorem

Extension of Novik and Browder's theorem

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 Bjorner-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.