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darijgr committed Apr 12, 2018
1 parent 7450608 commit 29c9278
Showing 1 changed file with 6 additions and 3 deletions.
9 changes: 6 additions & 3 deletions src/sage/combinat/chas/wqsym.py
Expand Up @@ -191,6 +191,9 @@ class WordQuasiSymmetricFunctions(UniqueRepresentation, Parent):
is implemented at
:class:`~sage.combinat.chas.wqsym.WordQuasiSymmetricFunctions.M`.
Other bases are the cone basis (aka C basis), the characteristic
basis (aka X basis), the Q basis and the Phi basis.
`WQSym` is endowed with a connected graded Hopf algebra structure (see
Section 2.2 of [NoThWi08]_, Section 1.1 of [FoiMal14]_ and
Section 4.3.2 of [MeNoTh11]_) given by
Expand Down Expand Up @@ -312,7 +315,7 @@ def a_realization(self):
"""
return self.M()

_shorthands = tuple(['M', 'X', 'C', 'Q'])
_shorthands = tuple(['M', 'X', 'C', 'Q', 'Phi'])

class M(WQSymBasis_abstract):
r"""
Expand Down Expand Up @@ -624,7 +627,7 @@ class Q(WQSymBasis_abstract):
.. MATH::
Q_P = \sum M_W,
Q_P = \sum \mathbf{M}_W,
where the sum is over ordered set partitions `W` satisfying
`P \leq W`.
Expand Down Expand Up @@ -819,7 +822,7 @@ class Phi(WQSymBasis_abstract):
.. MATH::
\Phi_P = \sum M_W,
\Phi_P = \sum \mathbf{M}_W,
where the sum is over ordered set partitions `W` satisfying
`W \leq P`.
Expand Down

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