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Is there any result which gives us a relation between f-vector of simplicial complex and f-vector of nonfaces of a simplicial complex?

Thank you

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    $\begingroup$ You posted this same question about 7 hours earlier: mathoverflow.net/questions/366005/… $\endgroup$
    – Sam Hopkins
    Jul 19, 2020 at 18:11
  • $\begingroup$ By a "nonface," do you mean any set of vertices that don't form a face or a minimal set of vertices that don't form a face? $\endgroup$
    – Richard Stanley
    Jul 20, 2020 at 1:08
  • $\begingroup$ A nonface means the face which are not present in the given simplicial complex. $\endgroup$
    – Iqra Khan
    Jul 20, 2020 at 9:07
  • $\begingroup$ Maybe I don't understand what you mean, but if a simplicial complex on $n$ vertices has $f_i$ $i$-dimensional faces, then it has ${n\choose i+1}-f_i$ $i$-dimensional nonfaces. $\endgroup$
    – Richard Stanley
    Aug 12, 2020 at 0:14

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