Maximal Projective Degrees for Strict Partitions

Let λ be a partition, and denote by f λ the number of standard tableaux of shape λ. The asymptotic shape of λ maximizing f λ was determined in the classical work of Logan and Shepp and, independently, of Vershik and Kerov. The analogue problem, where the number of parts of λ is bounded by a fixed number, was done by Askey and Regev – though some steps in this work were assumed without a proof. Here these steps are proved rigorously. When λ is strict, we denote by gλ the number of standard tableau of shifted shape λ. We determine the partition λ maximizing gλ in the strip. In addition we give a conjecture related to the maximizing of gλ without any length restrictions.