A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes
Tóm tắt
Stanley proved that for any centrally symmetric simplicial d-polytope P with
$$d\ge 3$$
,
$$g_2(P) \ge {d \atopwithdelims ()2}-d$$
. We provide a characterization of centrally symmetric simplicial d-polytopes with
$$d\ge 4$$
that satisfy this inequality as equality. This gives a natural generalization of the classical Lower Bound Theorem for simplicial polytopes to the setting of centrally symmetric simplicial polytopes.
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