Bijection classes for type \(B_n^{(1)}\).

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

AUTHORS:

  • Travis Scrimshaw (2012-12-21): Initial version

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()
class sage.combinat.rigged_configurations.bij_type_B.KRTToRCBijectionTypeB(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC

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

next_state(val)

Build the next state for type \(B_n^{(1)}\).

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)
other_outcome(rc, pos_val, width_n)

Do the other case \((QS)\) possibility.

This arises from the ambiguity when we found a singular string at the max width in \(\nu^{(n)}\). We had first attempted case \((S)\), and if that resulted in an invalid rigged configuration, we now finish the bijection using case \((QS)\).

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(verbose=False)

Run the bijection from a tensor product of KR tableaux to a rigged configuration.

INPUT:

  • tp_krt – A tensor product of KR tableaux
  • verbose – (Default: False) Display each step in the bijection

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
class sage.combinat.rigged_configurations.bij_type_B.RCToKRTBijectionTypeB(RC_element)

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 \(B_n^{(1)}\).

next_state(height)

Build the next state for type \(B_n^{(1)}\).

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(verbose=False)

Run the bijection from rigged configurations to tensor product of KR tableaux for type \(B_n^{(1)}\).

INPUT:

  • verbose – (Default: False) Display each step in the bijection

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]]

Previous topic

Bijection classes for type \(A_n^{(1)}\)

Next topic

Bijection classes for type \(C_n^{(1)}\).

This Page