The Cohen-Macaulay Property of $f$-ideals

A-Ming Liu, Jin Guo, Tongsuo Wu

For positive integers $d<n$, let $[n{]}_d=\{A\in 2^{[n]}\mid |A|=d\}$ where $[n]=:\{1,2,\dots ,n\}$. For a pure $f$-simplicial complex $\Delta$ such that $\dim (\Delta )=\dim ({\Delta }^c)$ an…