Kalai's 3^d-conjecture for unconditional and locally anti-blocking polytopes

08/05/2023
by   Raman Sanyal, et al.
0

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

Please sign up or login with your details

Forgot password? Click here to reset