Shellable Complexes from Multicomplexes

Abstract

Suppose a group $G$ acts properly on a simplicial complex $\Gamma$. Let $l$ be the number of $G$-invariant vertices and $p_1,p_2,...p_m$ be the sizes of the $G$-orbits having size greater than 1. Then $\Gamma$ must be a subcomplex of $\Lambda ={\Delta }^{l-1}\ast \partial {\Delta }^{p_1-1}\ast ...\ast \partial {\Delta }^{p_m-1}$. A result of Novik gives necessary conditions on the face numbers of Cohen-Macaulay subcomplexes of $\Lambda$. We show that these conditions are also sufficient, and thus provide a complete characterization of the face numbers of these complexes.

12 pages

Cited by in corpus (1)

• Face numbers of generalized balanced Cohen-Macaulay complexes