Maximal projective degrees for strict partitions
Summary: Let \(\lambda\) be a partition, and denote by \(f^\lambda\) the number of standard tableaux of shape \(\lambda\). The asymptotic shape of \(\lambda\) maximizing \(f^\lambda\) 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 \(\lambda\) 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 \(\lambda\) is strict, we denote by \(g^\lambda\) the number of standard tableau of shifted shape \(\lambda\). We determine the partition \(\lambda\) maximizing \(g^\lambda\) in the strip. In addition we give a conjecture related to the maximizing of \(g^\lambda\) without any length restrictions.
scientific article; zbMATH DE number 5540837