Kalai's 3^d-conjecture for unconditional and locally anti-blocking polytopes
Kalai's 3^d-conjecture states that every centrally symmetric d-polytope has at least 3^d faces. We give short proofs for two special cases: if P is unconditional (that is, invariant w.r.t. reflection in any coordinate hyperplane), and more generally, if P is locally anti-blocking (that is, looks like an unconditional polytope in every orthant). In both cases we show that the minimum is attained exactly for the Hanner polytopes.
READ FULL TEXT