Bijection classes for type \(D_4^{(3)}\).

Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(D_4^{(3)}\).

AUTHORS:

  • Travis Scrimshaw (2014-09-10): Initial version

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 3], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D_tri import KRTToRCBijectionTypeDTri
sage: bijection = KRTToRCBijectionTypeDTri(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['D', 4, 3], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D_tri import RCToKRTBijectionTypeDTri
sage: bijection = RCToKRTBijectionTypeDTri(RC(partition_list=[[],[]]))
sage: TestSuite(bijection).run()
class sage.combinat.rigged_configurations.bij_type_D_tri.KRTToRCBijectionTypeDTri(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA

Specific implementation of the bijection from KR tableaux to rigged configurations for type \(D_4^{(3)}\).

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

next_state(val)

Build the next state for type \(D_4^{(3)}\).

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 3], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_D_tri import KRTToRCBijectionTypeDTri
sage: bijection = KRTToRCBijectionTypeDTri(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_D_tri.RCToKRTBijectionTypeDTri(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 \(D_4^{(3)}\).

next_state(height)

Build the next state for type \(D_4^{(3)}\).

TESTS:

sage: RC = RiggedConfigurations(['D', 4, 3], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D_tri import RCToKRTBijectionTypeDTri
sage: bijection = RCToKRTBijectionTypeDTri(RC(partition_list=[[3],[2]]))
sage: bijection.next_state(1)
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