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
- 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 \(D_{n+1}^{(2)}\).
- 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 tableauxverbose
– (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() -1[ ]-1 0[ ]0 1[ ]1
- 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 \(D_{n+1}^{(2)}\).
- 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 bijectionbuild_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