Mod \(p\) Buchstaber Invariant

We investigate the \(\operatorname{mod}\,p\) Buchstaber invariant of the skeletons of simplices for a prime number \(p\) and compare such invariants for different values of \(p\) . For \(p=2\) , the invariant is the real Buchstaber invariant. Our findings reveal that their values are generally distinct. Additionally, we determine or estimate the \(\operatorname{mod}\,p\) Buchstaber invariants of certain universal simplicial complexes \(X(\mathbb F_p^n)\) .