Maximal projective degrees for strict partitions
type: Item
instance of: scholarly article
title: Maximal projective degrees for strict partitions
zbMATH Open document ID: 1158.05340
author: Anne Henke
author: Dan Bernstein
author: Amitai Regev
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/129720
full work available at URL: v14i1r59.html
review text: 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.
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 5540837
zbMATH Keywords: strict partitions
zbMATH Keywords: standard tableaux
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5540837