SFA::SfAOmega
--
applies the Omega-automorphism
SFA::SfAOmega(sfa <,alist>)
sfa | - | any symmetric function |
alist | - | a list of alphabets |
The SFA::SfAOmega
function applies the
Omega-automorphism to the symmetric function
sfa
.
This involution is defined as:
h[i](A) ->> e[i](A)
,
e[i](A) ->> h[i](A)
,
p[i](A) ->> (-1)^(i-1) p[i](A)
. In terms of Schur functions, the involution conjugates the indexing partition.
One can apply SFA::SfAOmega
solely on symmetric functions over the
alphabets given in the second parameter alist
.
>> muEC::SFA::SfAOmega( p[3,1](A1) - q*s[3](A2) );
p[3, 1](A1) - q s[1, 1, 1](A2)
>> muEC::SFA::SfAOmega( p[3,1](A1) - q*s[3](A2), [ A1 ]);
p[3, 1](A1) - q s[3](A2)
SYMF::SfOmega
, PART::Part2Conjugate
MuPAD Combinat, an open source algebraic combinatorics package