Bijection classes for type \(A_{2n}^{(2)\dagger}\).¶
Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(A_{2n}^{(2)\dagger}\).
AUTHORS:
- Travis Scrimshaw (2012-12-21): Initial version
TESTS:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(CartanType(['A', 4, 2]).dual(), [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import KRTToRCBijectionTypeA2Dual
sage: bijection = KRTToRCBijectionTypeA2Dual(KRT(pathlist=[[2,1]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(CartanType(['A', 4, 2]).dual(), [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import RCToKRTBijectionTypeA2Dual
sage: bijection = RCToKRTBijectionTypeA2Dual(RC(partition_list=[[],[]]))
sage: TestSuite(bijection).run()
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class
sage.combinat.rigged_configurations.bij_type_A2_dual.
KRTToRCBijectionTypeA2Dual
(tp_krt)¶ Bases:
sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC
Specific implementation of the bijection from KR tableaux to rigged configurations for type \(A_{2n}^{(2)\dagger}\).
This inherits from type \(C_n^{(1)}\) because we use the same methods in some places.
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next_state
(val)¶ Build the next state for type \(A_{2n}^{(2)\dagger}\).
TESTS:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(CartanType(['A', 4, 2]).dual(), [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import KRTToRCBijectionTypeA2Dual sage: bijection = KRTToRCBijectionTypeA2Dual(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, [2]) sage: bijection.next_state(2)
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class
sage.combinat.rigged_configurations.bij_type_A2_dual.
RCToKRTBijectionTypeA2Dual
(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 \(A_{2n}^{(2)\dagger}\).
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next_state
(height)¶ Build the next state for type \(A_{2n}^{(2)\dagger}\).
TESTS:
sage: RC = RiggedConfigurations(CartanType(['A', 4, 2]).dual(), [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import RCToKRTBijectionTypeA2Dual sage: bijection = RCToKRTBijectionTypeA2Dual(RC(partition_list=[[2],[2,2]])) sage: bijection.next_state(1) -1
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