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some edits to docs
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Anne Schilling authored and Travis Scrimshaw committed Dec 11, 2013
1 parent 877c215 commit 42bc8b6
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Expand Up @@ -761,7 +761,7 @@ def fermionic_formula(self, q=None, only_highest_weight=False, weight=None):
r"""
Return the fermoinic formula associated to ``self``.
Given a set of rigged configurations `RC(\Lambda, L)`, the fermonic
Given a set of rigged configurations `RC(\lambda, L)`, the fermonic
formula is defined as:
.. MATH::
Expand All @@ -780,8 +780,7 @@ def fermionic_formula(self, q=None, only_highest_weight=False, weight=None):
I \times \ZZ} \begin{bmatrix} p_i^{(a)} + m_i^{(a)} \\ m_i^{(a)}
\end{bmatrix}_q.
Here we consider a more general fermionic formula in the weight
algebra:
The generating function of `M(\lambda, L; q)` in the weight algebra subsumes all fermionic formulas:
.. MATH::
Expand All @@ -790,11 +789,11 @@ def fermionic_formula(self, q=None, only_highest_weight=False, weight=None):
This is conjecturally equal to the
:meth:`one dimensional configuration sum
<sage.combinat.crystals.tensor_product.CrystalOfWords.one_dimensional_configuration_sum>`
of the corresponding tensor product of Kirillov-Reshetikhin crystals.
of the corresponding tensor product of Kirillov-Reshetikhin crystals, see [HKOTT2002]_.
This has been proven in general for type `A_n^{(1)}` [BijectionLRT]_,
single factors `B^{r,s}` in type `D_n^{(1)}` [OSS2011]_ with the result
from [Sakamoto13]_, as well as for a tensor product of single columns
[OSS2003]_ or a tensor product of single rows [OSS03]_ for all
[OSS2003]_, [BijectionDn]_ or a tensor product of single rows [OSS03]_ for all
non-exceptional types.
INPUT:
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