Bijection classes for type \(B_n^{(1)}\).¶
Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(B_n^{(1)}\).
AUTHORS:
- Travis Scrimshaw (2012-12-21): Initial version
TESTS:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB
sage: bijection = KRTToRCBijectionTypeB(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['B', 3, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB
sage: bijection = RCToKRTBijectionTypeB(RC(partition_list=[[],[],[]]))
sage: TestSuite(bijection).run()
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class
sage.combinat.rigged_configurations.bij_type_B.
KRTToRCBijectionTypeB
(tp_krt)¶ Bases:
sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC
Specific implementation of the bijection from KR tableaux to rigged configurations for type \(B_n^{(1)}\).
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next_state
(val)¶ Build the next state for type \(B_n^{(1)}\).
TESTS:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB sage: bijection = KRTToRCBijectionTypeB(KRT(pathlist=[[-1,2]])) sage: bijection.cur_path.insert(0, []) sage: bijection.cur_dims.insert(0, [0, 1]) sage: bijection.cur_path[0].insert(0, [3]) sage: bijection.next_state(3)
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other_outcome
(rc, pos_val, width_n)¶ Do the other case \((QS)\) possibility.
This arises from the ambiguity when we found a singular string at the max width in \(\nu^{(n)}\). We had first attempted case \((S)\), and if that resulted in an invalid rigged configuration, we now finish the bijection using case \((QS)\).
EXAMPLES:
sage: RC = RiggedConfigurations(['B',3,1], [[2,1],[1,2]]) sage: rc = RC(partition_list=[[2,1], [2,1,1], [5,1]]) sage: t = rc.to_tensor_product_of_kirillov_reshetikhin_tableaux() sage: t.to_rigged_configuration() == rc # indirect doctest True
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run
(verbose=False)¶ Run the bijection from a tensor product of KR tableaux to a rigged configuration.
INPUT:
tp_krt
– A tensor product of KR tableauxverbose
– (Default:False
) Display each step in the bijection
EXAMPLES:
sage: from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[2, 1]]) sage: KRTToRCBijectionTypeB(KRT(pathlist=[[0,3]])).run() <BLANKLINE> 0[ ]0 <BLANKLINE> -1[ ]-1 -1[ ]-1 <BLANKLINE> 0[]0 <BLANKLINE> sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[3, 1]]) sage: KRTToRCBijectionTypeB(KRT(pathlist=[[-2,3,1]])).run() <BLANKLINE> (/) <BLANKLINE> -1[ ]-1 <BLANKLINE> 0[]0 <BLANKLINE>
TESTS:
Check that trac ticket #19384 is fixed:
sage: RC = RiggedConfigurations(['B',3,1], [[3,1],[3,1]]) sage: RC._test_bijection() sage: RC = RiggedConfigurations(['B',3,1], [[1,1],[3,1],[1,1]]) sage: RC._test_bijection()
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class
sage.combinat.rigged_configurations.bij_type_B.
RCToKRTBijectionTypeB
(RC_element)¶ Bases:
sage.combinat.rigged_configurations.bij_type_C.RCToKRTBijectionTypeC
Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(B_n^{(1)}\).
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next_state
(height)¶ Build the next state for type \(B_n^{(1)}\).
TESTS:
sage: RC = RiggedConfigurations(['B', 3, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB sage: bijection = RCToKRTBijectionTypeB(RC(partition_list=[[1],[1,1],[1]])) sage: bijection.next_state(0) 0
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run
(verbose=False, build_graph=False)¶ Run the bijection from rigged configurations to tensor product of KR tableaux for type \(B_n^{(1)}\).
INPUT:
verbose
– (default:False
) display each step in the bijectionbuild_graph
– (default:False
) build the graph of each step of the bijection
EXAMPLES:
sage: RC = RiggedConfigurations(['B', 3, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB sage: RCToKRTBijectionTypeB(RC(partition_list=[[1],[1,1],[1]])).run() [[3], [0]] sage: RC = RiggedConfigurations(['B', 3, 1], [[3, 1]]) sage: x = RC(partition_list=[[],[1],[1]]) sage: RCToKRTBijectionTypeB(x).run() [[1], [3], [-2]] sage: bij = RCToKRTBijectionTypeB(x) sage: bij.run(build_graph=True) [[1], [3], [-2]] sage: bij._graph Digraph on 6 vertices
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