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SG::SgCharTable -- computes the table of characters

Call(s)


SG::SgCharTable(n <,part1> <,part2>)
SG::SgCharTable(n <,index>)

Parameters

n- any positive integer denoting the degree of a symmetric group
part1, part2- any lists denoting partitions

Introduction

The SG::SgCharTable gives the table of characters for the symmetric group of order n. Let t be this matrix, part1, part2 be two partitions of n, of index i, j in the list of partitions SG::SgCharTable(n, index), then t[i,j] is equal to the value of the irreducible character of index part1 on the conjugacy class indexed by part2.

Example 1

>> muEC::SG::SgCharTable( 3 );
                              +-           -+
                              |   1,  1, 1  |
                              |             |
                              |  -1,  0, 2  |
                              |             |
                              |   1, -1, 1  |
                              +-           -+
>> muEC::SG::SgCharTable( 3, index );
                         [[3], [2, 1], [1, 1, 1]]
>> muEC::SG::SgCharTable(3, [2,1], [1,1,1]);
                                     2

Related Functions

TYP::IsPart

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MuPAD Combinat, an open source algebraic combinatorics package