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# 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)
        5

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