Convexity of the permanent for doubly stochastic matrices

Let Ω _n denote the set of all n×n doubly stochastic matrices and let J_n denote the n×n matrix all of whose entries are 1/n. Lih and Wang conjectuted that per(1?i)J_n +iA≤(1?i)perJ_n 1i perA for all A∈Ω _n and all t∈0,1/2], and proved their conjecture for n=3. In this paper we propose a similar conjecture asserting that for any A∈Ω _n \{J_n }, the permanent function is strietly convex on the straight line segment joining J_n and (J_n +A)/2, and prove it for the case n=3.