Bijection classes for type \(A_{2n-1}^{(2)}\).¶
Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(A_{2n-1}^{(2)}\).
AUTHORS:
- Travis Scrimshaw (2012-12-21): Initial version
TESTS:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 5, 2], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd
sage: bijection = KRTToRCBijectionTypeA2Odd(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['A', 5, 2], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd
sage: bijection = RCToKRTBijectionTypeA2Odd(RC(partition_list=[[],[],[]]))
sage: TestSuite(bijection).run()
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class
sage.combinat.rigged_configurations.bij_type_A2_odd.
KRTToRCBijectionTypeA2Odd
(tp_krt)¶ Bases:
sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA
Specific implementation of the bijection from KR tableaux to rigged configurations for type \(A_{2n-1}^{(2)}\).
This inherits from type \(A_n^{(1)}\) because we use the same methods in some places.
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next_state
(val)¶ Build the next state for type \(A_{2n-1}^{(2)}\).
TESTS:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 5, 2], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd sage: bijection = KRTToRCBijectionTypeA2Odd(KRT(pathlist=[[-2,3]])) 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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class
sage.combinat.rigged_configurations.bij_type_A2_odd.
RCToKRTBijectionTypeA2Odd
(RC_element)¶ Bases:
sage.combinat.rigged_configurations.bij_type_A.RCToKRTBijectionTypeA
Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(A_{2n-1}^{(2)}\).
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next_state
(height)¶ Build the next state for type \(A_{2n-1}^{(2)}\).
TESTS:
sage: RC = RiggedConfigurations(['A', 5, 2], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd sage: bijection = RCToKRTBijectionTypeA2Odd(RC(partition_list=[[1],[2,1],[2]])) sage: bijection.next_state(0) -2
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