Monotone separations for constant degree polynomials

We prove a separation between monotone and general arithmetic formulas for polynomials of constant degree. We give an example of a polynomial C in n variables and degree k which is computable by a homogeneous arithmetic formula of size O(k2n2), but every monotone formula computing C requires size (n/kc)Ω(log k), with c ∈ (0, 1). Since the upper bound is achieved by a homogeneous arithmetic formula, we also obtain a separation between monotone and homogeneous formulas, for polynomials of constant degree.