Abstract classes for the rigged configuration bijections¶
This file contains two sets of classes, one for the bijection from KR tableaux to rigged configurations and the other for the reverse bijection. We do this for two reasons, one is because we can store a state in the bijection locally, so we do not have to constantly pass it around between functions. The other is because it makes the code easier to read in the *_element.py files.
These classes are not meant to be used by the user and are only supposed to be
used internally to perform the bijections between
TensorProductOfKirillovReshetikhinTableaux
and RiggedConfigurations
.
AUTHORS:
Travis Scrimshaw (2011-04-15): Initial version
- class sage.combinat.rigged_configurations.bij_abstract_class.KRTToRCBijectionAbstract(tp_krt)¶
Bases:
object
Root abstract class for the bijection from KR tableaux to rigged configurations.
This class holds the state of the bijection and generates the next state. This class should never be created directly.
- next_state(val)¶
Build the next state in the bijection.
INPUT:
val
– The value we are adding
- run(verbose=False)¶
Run the bijection from a tensor product of KR tableaux to a rigged configuration.
INPUT:
tp_krt
– A tensor product of KR tableauxverbose
– (Default:False
) Display each step in the bijection
EXAMPLES:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA sage: KRTToRCBijectionTypeA(KRT(pathlist=[[5,2]])).run() -1[ ]-1 1[ ]1 0[ ]0 -1[ ]-1
- class sage.combinat.rigged_configurations.bij_abstract_class.RCToKRTBijectionAbstract(RC_element)¶
Bases:
object
Root abstract class for the bijection from rigged configurations to tensor product of Kirillov-Reshetikhin tableaux.
This class holds the state of the bijection and generates the next state. This class should never be created directly.
- next_state(height)¶
Build the next state in the bijection.
- run(verbose=False, build_graph=False)¶
Run the bijection from rigged configurations to tensor product of KR tableaux.
INPUT:
verbose
– (default:False
) display each step in the bijectionbuild_graph
– (default:False
) build the graph of each step of the bijection
EXAMPLES:
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]]) sage: x = RC(partition_list=[[1],[1],[1],[1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA sage: RCToKRTBijectionTypeA(x).run() [[2], [5]] sage: bij = RCToKRTBijectionTypeA(x) sage: bij.run(build_graph=True) [[2], [5]] sage: bij._graph Digraph on 3 vertices