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# Bijection classes for type \(D_{n+1}^{(2)}\).

Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(D_{n+1}^{(2)}\).

AUTHORS:

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

TESTS:

    sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 2], [[2,1]])
    sage: from sage.combinat.rigged_configurations.bij_type_D_twisted import KRTToRCBijectionTypeDTwisted
    sage: bijection = KRTToRCBijectionTypeDTwisted(KRT(pathlist=[[-1,2]]))
    sage: TestSuite(bijection).run()
    sage: RC = RiggedConfigurations(['D', 4, 2], [[2, 1]])
    sage: from sage.combinat.rigged_configurations.bij_type_D_twisted import RCToKRTBijectionTypeDTwisted
    sage: bijection = RCToKRTBijectionTypeDTwisted(RC())
    sage: TestSuite(bijection).run()

class `sage.combinat.rigged_configurations.bij_type_D_twisted.``KRTToRCBijectionTypeDTwisted`(tp_krt)

  Bases: `sage.combinat.rigged_configurations.bij_type_D.KRTToRCBijectionTypeD`, `sage.combinat.rigged_configurations.bij_type_A2_even.KRTToRCBijectionTypeA2Even`

  Specific implementation of the bijection from KR tableaux to rigged configurations for type \(D_{n+1}^{(2)}\).

  This inherits from type \(C_n^{(1)}\) and \(D_n^{(1)}\) because we use the same methods in some places.

  `next_state`(val)

    Build the next state for type \(D_{n+1}^{(2)}\).

    TESTS:

        sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 2], [[2,1]])
        sage: from sage.combinat.rigged_configurations.bij_type_D_twisted import KRTToRCBijectionTypeDTwisted
        sage: bijection = KRTToRCBijectionTypeDTwisted(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)

  `run`(verbose=False)

    Run the bijection from a tensor product of KR tableaux to a rigged configuration for type \(D_{n+1}^{(2)}\).

    INPUT:

    - `tp_krt` – A tensor product of KR tableaux
    - `verbose` – (Default: `False`) Display each step in the bijection

    EXAMPLES:

        sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 2], [[3,1]])
        sage: from sage.combinat.rigged_configurations.bij_type_D_twisted import KRTToRCBijectionTypeDTwisted
        sage: KRTToRCBijectionTypeDTwisted(KRT(pathlist=[[-1,3,2]])).run()
        <BLANKLINE>
        -1[ ]-1
        <BLANKLINE>
        0[ ]0
        <BLANKLINE>
        1[ ]1
        <BLANKLINE>

class `sage.combinat.rigged_configurations.bij_type_D_twisted.``RCToKRTBijectionTypeDTwisted`(RC_element)

  Bases: `sage.combinat.rigged_configurations.bij_type_D.RCToKRTBijectionTypeD`, `sage.combinat.rigged_configurations.bij_type_A2_even.RCToKRTBijectionTypeA2Even`

  Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(D_{n+1}^{(2)}\).

  `next_state`(height)

    Build the next state for type \(D_{n+1}^{(2)}\).

    TESTS:

        sage: RC = RiggedConfigurations(['D', 4, 2], [[2, 1]])
        sage: from sage.combinat.rigged_configurations.bij_type_D_twisted import RCToKRTBijectionTypeDTwisted
        sage: bijection = RCToKRTBijectionTypeDTwisted(RC(partition_list=[[2],[2,2],[2,2]]))
        sage: bijection.next_state(0)
        -1

  `run`(verbose=False, build_graph=False)

    Run the bijection from rigged configurations to tensor product of KR tableaux for type \(D_{n+1}^{(2)}\).

    INPUT:

    - `verbose` – (default: `False`) display each step in the bijection
    - `build_graph` – (default: `False`) build the graph of each step of the bijection

    EXAMPLES:

        sage: RC = RiggedConfigurations(['D', 4, 2], [[3, 1]])
        sage: x = RC(partition_list=[[],[1],[1]])
        sage: from sage.combinat.rigged_configurations.bij_type_D_twisted import RCToKRTBijectionTypeDTwisted
        sage: RCToKRTBijectionTypeDTwisted(x).run()
        [[1], [3], [-2]]
        sage: bij = RCToKRTBijectionTypeDTwisted(x)
        sage: bij.run(build_graph=True)
        [[1], [3], [-2]]
        sage: bij._graph
        Digraph on 6 vertices

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