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

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

AUTHORS:

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

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['C', 3, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_C import KRTToRCBijectionTypeC
sage: bijection = KRTToRCBijectionTypeC(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['C', 3, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_C import RCToKRTBijectionTypeC
sage: bijection = RCToKRTBijectionTypeC(RC(partition_list=[[],[],[]]))
sage: TestSuite(bijection).run()

class sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA

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

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

next_state(val)

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

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['C', 3, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_C import KRTToRCBijectionTypeC
sage: bijection = KRTToRCBijectionTypeC(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)

class sage.combinat.rigged_configurations.bij_type_C.RCToKRTBijectionTypeC(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 \(C_n^{(1)}\).

next_state(height)

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

TESTS:

sage: RC = RiggedConfigurations(['C', 3, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_C import RCToKRTBijectionTypeC
sage: bijection = RCToKRTBijectionTypeC(RC(partition_list=[[2],[2],[1]]))
sage: bijection.next_state(0)
-1