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SYMF::Char2Sf -- converts a virtual character into a symmetric function

Call(s)


SYMF::Char2Sf(expr)

Parameters

expr- any linear combination of cl[part] for any partition part

Introduction

The SYMF::Char2Sf function converts a virtual character into a symmetric function expressed on p-basis.

We denote by cl[part], where part is a partition, the class function on the symmetric group that is evaluated to 1 for permutations with cycletype part, and 0 otherwise.

The SYMF::Char2Sf function realizes the isomorphism between class functions on the symmetric group of degree n and homogeneous symmetric functions of degree n.

Example 1

>> muEC::SYMF::Char2Sf( cl[5,3,1,1] )
                               p[5, 3, 1, 1]
                               -------------
                                     30

Related Functions

SfInternal, SfPlethysm, Sf2Char, SfZee

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MuPAD Combinat, an open source algebraic combinatorics package