A plethysm formula for \(p_ \mu(\underline x)\circ h_ \lambda(\underline x)\)
type: Item
instance of: scholarly article
title: A plethysm formula for \(p_ \mu(\underline x)\circ h_ \lambda(\underline x)\)
zbMATH Open document ID: 0885.05108
author: William F. IV Doran
published in: The Electronic Journal of Combinatorics
publication date: 1998-02-12T00:00:00Z
review text: Summary: This paper gives a new formula for the plethysm of power-sum symmetric functions and complete symmetric functions. The form of the main result is that for \(\mu \vdash b\) and \(\lambda \vdash a\) with length \(t\), \[ p_\mu(\underline{x}) \circ h_\lambda(\underline{x}) = \sum_T \underline{\omega}^{\text{maj}_{\mu^t} (T)} s_{\text{sh}(T)} (\underline{x}) \] where the sum is over semistandard tableaux of weight \(\lambda_1^b \lambda_2^b \dots \lambda_t^b\) and \(\underline{\omega}^{\text{maj}_{\mu^t} (T)}\) is a root of unity which depends on \(\mu\), \(t\), and \(T\).
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 1117999
zbMATH Keywords: plethysm
zbMATH Keywords: symmetric functions
zbMATH Keywords: tableaux
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1117999