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

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

AUTHORS:

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

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 2], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_even import KRTToRCBijectionTypeA2Even
sage: bijection = KRTToRCBijectionTypeA2Even(KRT(pathlist=[[-1,2]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(['A', 4, 2], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_even import RCToKRTBijectionTypeA2Even
sage: bijection = RCToKRTBijectionTypeA2Even(RC(partition_list=[[],[]]))
sage: TestSuite(bijection).run()
class sage.combinat.rigged_configurations.bij_type_A2_even.KRTToRCBijectionTypeA2Even(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC

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

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

next_state(val)

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

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 2], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_even import KRTToRCBijectionTypeA2Even
sage: bijection = KRTToRCBijectionTypeA2Even(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_A2_even.RCToKRTBijectionTypeA2Even(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 \(A_{2n}^{(2)}\).

next_state(height)

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

TESTS:

sage: RC = RiggedConfigurations(['A', 4, 2], [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_even import RCToKRTBijectionTypeA2Even
sage: bijection = RCToKRTBijectionTypeA2Even(RC(partition_list=[[2],[2,2]]))
sage: bijection.next_state(1)
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