Part of the (internal) classes which runs the bijection between rigged
configurations and KR tableaux of type .
AUTHORS:
TESTS:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD
sage: bijection = KRTToRCBijectionTypeD(KRT(pathlist=[[3, 2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['D', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: bijection = RCToKRTBijectionTypeD(RC(partition_list=[[],[],[],[]]))
sage: TestSuite(bijection).run()
Bases: sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA
Specific implementation of the bijection from KR tableaux to rigged
configurations for type .
This inherits from type because we use the same methods in
some places.
Perform the doubling map of the rigged configuration at the current state of the bijection.
This is the map which
doubles each of the rigged partitions and updates the vacancy numbers
accordingly.
TESTS:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[4,1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD
sage: bijection = KRTToRCBijectionTypeD(KRT(pathlist=[[-1,4,3,2]]))
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)
sage: bijection.ret_rig_con
-2[ ]-2
(/)
(/)
(/)
sage: bijection.cur_dims
[[0, 1]]
sage: bijection.doubling_map()
sage: bijection.ret_rig_con
-4[ ][ ]-4
(/)
(/)
(/)
sage: bijection.cur_dims
[[0, 2]]
Perform the halving map of the rigged configuration at the current state of the bijection.
This is the inverse map to
which halves each of the rigged partitions and updates the vacancy
numbers accordingly.
TESTS:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[4,1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD
sage: bijection = KRTToRCBijectionTypeD(KRT(pathlist=[[-1,4,3,2]]))
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)
sage: test = bijection.ret_rig_con
sage: bijection.doubling_map()
sage: bijection.halving_map()
sage: test == bijection.ret_rig_con
True
Build the next state for type .
TESTS:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD
sage: bijection = KRTToRCBijectionTypeD(KRT(pathlist=[[5,3]]))
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)
Run the bijection from a tensor product of KR tableaux to a rigged
configuration for type .
INPUT:
EXAMPLES:
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD
sage: KRTToRCBijectionTypeD(KRT(pathlist=[[-3,2]])).run()
-1[ ]-1
2[ ]2
-1[ ]-1
-1[ ]-1
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 .
Perform the doubling map of the rigged configuration at the current state of the bijection.
This is the map which
doubles each of the rigged partitions and updates the vacancy numbers
accordingly.
TESTS:
sage: RC = RiggedConfigurations(['D', 4, 1], [[4, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: bijection = RCToKRTBijectionTypeD(RC(partition_list=[[],[],[],[1]]))
sage: bijection.cur_partitions
[(/)
, (/)
, (/)
, -1[ ]-1
]
sage: bijection.doubling_map()
sage: bijection.cur_partitions
[(/)
, (/)
, (/)
, -2[ ][ ]-2
]
Perform the halving map of the rigged configuration at the current state of the bijection.
This is the inverse map to
which halves each of the rigged partitions and updates the vacancy
numbers accordingly.
TESTS:
sage: RC = RiggedConfigurations(['D', 4, 1], [[4, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: bijection = RCToKRTBijectionTypeD(RC(partition_list=[[],[],[],[1]]))
sage: test = bijection.cur_partitions
sage: bijection.doubling_map()
sage: bijection.halving_map()
sage: test == bijection.cur_partitions
True
Build the next state for type .
TESTS:
sage: RC = RiggedConfigurations(['D', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: bijection = RCToKRTBijectionTypeD(RC(partition_list=[[],[1,1],[1],[1]]))
sage: bijection.next_state(0)
1
Run the bijection from rigged configurations to tensor product of KR
tableaux for type .
INPUT:
EXAMPLES:
sage: RC = RiggedConfigurations(['D', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
sage: RCToKRTBijectionTypeD(RC(partition_list=[[1],[1],[1],[1]])).run()
[[2], [-3]]