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