Abstract
Suppose a group G acts properly on a simplicial complex Γ. 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 Γ must be a subcomplex of \(\varLambda=\varDelta ^{l-1}*\partial \varDelta ^{p_{1}-1} *\cdots*\partial \varDelta ^{p_{m}-1}\). A result of Novik gives necessary conditions on the face numbers of Cohen–Macaulay subcomplexes of Λ. We show that these conditions are also sufficient, and thus provide a complete characterization of the face numbers of these complexes.
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