# Bijection classes for type $$D_n^{(1)}$$¶

Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type $$D_n^{(1)}$$.

AUTHORS:

• Travis Scrimshaw (2011-04-15): Initial version

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=[[-2, 3]]))
sage: TestSuite(bijection).run()
```
class sage.combinat.rigged_configurations.bij_type_D.KRTToRCBijectionTypeD(krt)¶

Bases: sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA

Specific implementation of the bijection from KR tableaux to rigged configurations for type $$D_n^{(1)}$$.

This inherits from type $$A_n^{(1)}$$ because we use the same methods in some places.

doubling_map()¶

Perform the doubling map of the rigged configuration at the current state of the bijection.

This is the map $$B(\Lambda) \hookrightarrow B(2 \Lambda)$$ 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]]
```
halving_map()¶

Perform the halving map of the rigged configuration at the current state of the bijection.

This is the inverse map to $$B(\Lambda) \hookrightarrow B(2 \Lambda)$$ 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
```
next_state(val)¶

Build the next state for type $$D_n^{(1)}$$.

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=[[-2, 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)
sage: bijection.ret_rig_con

-1[ ]-1

-1[ ]-1

(/)

(/)
```
class sage.combinat.rigged_configurations.bij_type_D.RCToKRTBijectionTypeD(RC_element)¶

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 $$D_n^{(1)}$$.

doubling_map()¶

Perform the doubling map of the rigged configuration at the current state of the bijection.

This is the map $$B(\Lambda) \hookrightarrow B(2 \Lambda)$$ 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
]
```
halving_map()¶

Perform the halving map of the rigged configuration at the current state of the bijection.

This is the inverse map to $$B(\Lambda) \hookrightarrow B(2 \Lambda)$$ 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
```
next_state(height)¶

Build the next state for type $$D_n^{(1)}$$.

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(1)
-2
sage: bijection.cur_partitions
[(/)
, (/)
, (/)
, (/)
]
```

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