### Navigation

- index
- modules |
- next |
- previous |
- Combinatorics »
- Rigged Configurations »
- Rigged Configuration Bijections »

# 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()

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.

  `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)

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 \(A_{2n}^{(2)\dagger}\).

  `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

### Navigation

- index
- modules |
- next |
- previous |
- Combinatorics »
- Rigged Configurations »
- Rigged Configuration Bijections »