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 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()

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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 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