SYMF::Char2Sf
--
converts a virtual character into a symmetric function
SYMF::Char2Sf(expr)
expr | - | any linear combination of cl[part] for any partition part |
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
.
>> muEC::SYMF::Char2Sf( cl[5,3,1,1] )
p[5, 3, 1, 1] ------------- 30
SfInternal
, SfPlethysm
, Sf2Char
, SfZee
MuPAD Combinat, an open source algebraic combinatorics package