Bijection classes for type \(D_n^{(1)}\)¶
Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(D_n^{(1)}\).
AUTHORS:
- Travis Scrimshaw (2011-04-15): Initial version 
- class sage.combinat.rigged_configurations.bij_type_D.KRTToRCBijectionTypeD(tp_krt)[source]¶
- Bases: - KRTToRCBijectionTypeA- Specific implementation of the bijection from KR tableaux to rigged configurations for type \(D_n^{(1)}\). - This inherits from type \(A_n^{(1)}\) because we use the same methods in some places. - doubling_map()[source]¶
- Perform the doubling map of the rigged configuration at the current state of the bijection. - This is the map \(B(\Lambda) \hookrightarrow B(2 \Lambda)\) which doubles each of the rigged partitions and updates the vacancy numbers accordingly. 
 - halving_map()[source]¶
- Perform the halving map of the rigged configuration at the current state of the bijection. - This is the inverse map to \(B(\Lambda) \hookrightarrow B(2 \Lambda)\) which halves each of the rigged partitions and updates the vacancy numbers accordingly. 
 - run(verbose=False)[source]¶
- Run the bijection from a tensor product of KR tableaux to a rigged configuration for type \(D_n^{(1)}\). - INPUT: - tp_krt– a tensor product of KR tableaux
- verbose– (default:- False) display each step in the bijection
 - EXAMPLES: - sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD sage: KRTToRCBijectionTypeD(KRT(pathlist=[[-3,2]])).run() -1[ ]-1 2[ ]2 -1[ ]-1 -1[ ]-1 - >>> from sage.all import * >>> KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', Integer(4), Integer(1)], [[Integer(2),Integer(1)]]) >>> from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD >>> KRTToRCBijectionTypeD(KRT(pathlist=[[-Integer(3),Integer(2)]])).run() <BLANKLINE> -1[ ]-1 <BLANKLINE> 2[ ]2 <BLANKLINE> -1[ ]-1 <BLANKLINE> -1[ ]-1 <BLANKLINE> 
 
- class sage.combinat.rigged_configurations.bij_type_D.RCToKRTBijectionTypeD(RC_element)[source]¶
- Bases: - RCToKRTBijectionTypeA- Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(D_n^{(1)}\). - doubling_map()[source]¶
- Perform the doubling map of the rigged configuration at the current state of the bijection. - This is the map \(B(\Lambda) \hookrightarrow B(2 \Lambda)\) which doubles each of the rigged partitions and updates the vacancy numbers accordingly. 
 - halving_map()[source]¶
- Perform the halving map of the rigged configuration at the current state of the bijection. - This is the inverse map to \(B(\Lambda) \hookrightarrow B(2 \Lambda)\) which halves each of the rigged partitions and updates the vacancy numbers accordingly. 
 - run(verbose=False, build_graph=False)[source]¶
- Run the bijection from rigged configurations to tensor product of KR tableaux for type \(D_n^{(1)}\). - INPUT: - verbose– boolean (default:- False); display each step in the bijection
- build_graph– boolean (default:- False); build the graph of each step of the bijection
 - EXAMPLES: - sage: RC = RiggedConfigurations(['D', 4, 1], [[2, 1]]) sage: x = RC(partition_list=[[1],[1],[1],[1]]) sage: from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD sage: RCToKRTBijectionTypeD(x).run() [[2], [-3]] sage: bij = RCToKRTBijectionTypeD(x) sage: bij.run(build_graph=True) [[2], [-3]] sage: bij._graph Digraph on 3 vertices - >>> from sage.all import * >>> RC = RiggedConfigurations(['D', Integer(4), Integer(1)], [[Integer(2), Integer(1)]]) >>> x = RC(partition_list=[[Integer(1)],[Integer(1)],[Integer(1)],[Integer(1)]]) >>> from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD >>> RCToKRTBijectionTypeD(x).run() [[2], [-3]] >>> bij = RCToKRTBijectionTypeD(x) >>> bij.run(build_graph=True) [[2], [-3]] >>> bij._graph Digraph on 3 vertices