Bijection classes for type \(A_{2n-1}^{(2)}\).

Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(A_{2n-1}^{(2)}\).

AUTHORS:

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

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 5, 2], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd
sage: bijection = KRTToRCBijectionTypeA2Odd(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['A', 5, 2], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd
sage: bijection = RCToKRTBijectionTypeA2Odd(RC(partition_list=[[],[],[]]))
sage: TestSuite(bijection).run()

class sage.combinat.rigged_configurations.bij_type_A2_odd.KRTToRCBijectionTypeA2Odd(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA

Specific implementation of the bijection from KR tableaux to rigged configurations for type \(A_{2n-1}^{(2)}\).

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 \(A_{2n-1}^{(2)}\).

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 5, 2], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd
sage: bijection = KRTToRCBijectionTypeA2Odd(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)

class sage.combinat.rigged_configurations.bij_type_A2_odd.RCToKRTBijectionTypeA2Odd(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 \(A_{2n-1}^{(2)}\).

next_state(height)

Build the next state for type \(A_{2n-1}^{(2)}\).

TESTS:

sage: RC = RiggedConfigurations(['A', 5, 2], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd
sage: bijection = RCToKRTBijectionTypeA2Odd(RC(partition_list=[[1],[2,1],[2]]))
sage: bijection.next_state(0)
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