Maximal projective degrees for strict partitions
The electronic journal of combinatorics, Tome 14 (2007)
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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.
D. Bernstein; A. Henke; A. Regev. Maximal projective degrees for strict partitions. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/977
@article{10_37236_977,
author = {D. Bernstein and A. Henke and A. Regev},
title = {Maximal projective degrees for strict partitions},
journal = {The electronic journal of combinatorics},
year = {2007},
volume = {14},
doi = {10.37236/977},
zbl = {1158.05340},
url = {http://geodesic.mathdoc.fr/articles/10.37236/977/}
}
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