Lower bounds for the Chvátal–Gomory rank in the 0/1 cube

We revisit the method of Chvátal, Cook, and Hartmann to establish lower bounds on the Chvátal–Gomory rank, and develop a simpler method. We provide new families of polytopes in the 0/1 cube with high rank, and we describe a deterministic family achieving a rank of at least (1+1/e)n−1>n(1+1/e)n−1>n. Finally, we show how integrality gaps lead to lower bounds.