degree(ClassFunction) -- Degree of virtual character

Function: degree

Description

For a virtual character ch of a symmetric group on n letters, the degree of ch is n.

i1 : S = schurRing(s,5);

i2 : ch = classFunction s_(3,1,1)

o2 = ClassFunction{{1, 1, 1, 1, 1} => 6}
                   {2, 2, 1} => -2
                   {5} => 1

o2 : ClassFunction

i3 : degree ch

o3 = 5

The degree of classFunction(s_\lambda) always agrees with |\lambda|:

i4 : lam = {4,2,1};

i5 : degree classFunction(new Partition from lam) == sum lam

o5 = true

A sum of characters of the same S_n keeps the same degree -- mixing distinct partitions of 5 still yields a class function of degree 5:

i6 : R = symmetricRing(QQ,5);

i7 : mix = classFunction(jacobiTrudi({4,1},R)) + 2*classFunction(jacobiTrudi({3,2},R));

i8 : degree mix

o8 = 5

Ways to use this method:

degree(ClassFunction) -- Degree of virtual character

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SchurRings.m2:7084:0.