Part of the (internal) classes which runs the bijection between rigged
configurations and KR tableaux of type .
AUTHORS:
TESTS:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB
sage: bijection = KRTToRCBijectionTypeB(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['B', 3, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB
sage: bijection = RCToKRTBijectionTypeB(RC(partition_list=[[],[],[]]))
sage: TestSuite(bijection).run()
Bases: sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC
Specific implementation of the bijection from KR tableaux to rigged
configurations for type .
Build the next state for type .
TESTS:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB
sage: bijection = KRTToRCBijectionTypeB(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, [3])
sage: bijection.next_state(3)
Do the other case possibility.
This arises from the ambiguity when we found a singular string at the
max width in . We had first attempted case
, and if
that resulted in an invalid rigged configuration, we now
finish the bijection using case
.
EXAMPLES:
sage: RC = RiggedConfigurations(['B',3,1], [[2,1],[1,2]])
sage: rc = RC(partition_list=[[2,1], [2,1,1], [5,1]])
sage: t = rc.to_tensor_product_of_kirillov_reshetikhin_tableaux()
sage: t.to_rigged_configuration() == rc # indirect doctest
True
Run the bijection from a tensor product of KR tableaux to a rigged configuration.
INPUT:
EXAMPLES:
sage: from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[2, 1]])
sage: KRTToRCBijectionTypeB(KRT(pathlist=[[0,3]])).run()
0[ ]0
-1[ ]-1
-1[ ]-1
0[]0
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['B', 3, 1], [[3, 1]])
sage: KRTToRCBijectionTypeB(KRT(pathlist=[[-2,3,1]])).run()
(/)
-1[ ]-1
0[]0
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 .
Build the next state for type .
TESTS:
sage: RC = RiggedConfigurations(['B', 3, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB
sage: bijection = RCToKRTBijectionTypeB(RC(partition_list=[[1],[1,1],[1]]))
sage: bijection.next_state(0)
0
Run the bijection from rigged configurations to tensor product of KR
tableaux for type .
INPUT:
EXAMPLES:
sage: RC = RiggedConfigurations(['B', 3, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB
sage: RCToKRTBijectionTypeB(RC(partition_list=[[1],[1,1],[1]])).run()
[[3], [0]]
sage: RC = RiggedConfigurations(['B', 3, 1], [[3, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB
sage: RCToKRTBijectionTypeB(RC(partition_list=[[],[1],[1]])).run()
[[1], [3], [-2]]