Combinatorics of polytopes with a group of linear symmetries of prime power order
The author extends the results of \textit{R. P. Stanley} [Graphs Comb. 3, 55--66 (1987; Zbl 0611.52002)] and \textit{R. M. Adin} [Adv. Math. 115, No. 2, 269--285 (1995; Zbl 0843.52006)] on lower bounds for the \(h\)-vector of rational simplicial \(d\)-polytopes \(P\) to the case that \(P\) is equipped with a proper linear action of a cyclic group \(G\) of prime power order. The action of a group \(G\) on a simplicial complex \(\Delta\) is said to be proper if \(\{S \in \Delta : \forall g \in H (S^g = S)\}\) is a simplicial complex for every subgroup \(H\) of \(G\).
scientific article; zbMATH DE number 2038452