Bijection classes for type \(A_n^{(1)}\)#
Part of the (internal) classes which run the bijection between rigged configurations and tensor products of Kirillov-Reshetikhin tableaux of type \(A_n^{(1)}\).
AUTHORS:
Travis Scrimshaw (2011-04-15): Initial version
- class sage.combinat.rigged_configurations.bij_type_A.KRTToRCBijectionTypeA(tp_krt)#
Bases:
sage.combinat.rigged_configurations.bij_abstract_class.KRTToRCBijectionAbstract
Specific implementation of the bijection from KR tableaux to rigged configurations for type \(A_n^{(1)}\).
- next_state(val)#
Build the next state for type \(A_n^{(1)}\).
EXAMPLES:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[4,3]])) 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_A.RCToKRTBijectionTypeA(RC_element)#
Bases:
sage.combinat.rigged_configurations.bij_abstract_class.RCToKRTBijectionAbstract
Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(A_n^{(1)}\).
- next_state(height)#
Build the next state for type \(A_n^{(1)}\).
EXAMPLES:
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA sage: bijection = RCToKRTBijectionTypeA(RC(partition_list=[[1],[1],[1],[1]])) sage: bijection.next_state(1) 5