Bijection classes for type \(A_n^{(1)}\)

Part of the (internal) classes which run the bijection between rigged configurations and tensor products of Kirillov-Reshetikhin tableaux of type \(A_n^{(1)}\).

AUTHORS:

  • Travis Scrimshaw (2011-04-15): Initial version

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA
sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[5,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA
sage: bijection = RCToKRTBijectionTypeA(RC(partition_list=[[],[],[],[]]))
sage: TestSuite(bijection).run()
class sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_abstract_class.KRTToRCBijectionAbstract

Specific implementation of the bijection from KR tableaux to rigged configurations for type \(A_n^{(1)}\).

next_state(val)

Build the next state for type \(A_n^{(1)}\).

EXAMPLES:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA
sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[4,3]]))
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)
class sage.combinat.rigged_configurations.bij_type_A.RCToKRTBijectionTypeA(RC_element)

Bases: sage.combinat.rigged_configurations.bij_abstract_class.RCToKRTBijectionAbstract

Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(A_n^{(1)}\).

next_state(height)

Build the next state for type \(A_n^{(1)}\).

EXAMPLES:

sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA
sage: bijection = RCToKRTBijectionTypeA(RC(partition_list=[[1],[1],[1],[1]]))
sage: bijection.next_state(0)
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Bijection classes for type \(B_n^{(1)}\).

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