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: 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

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)

Python

>>> from sage.all import *
>>> KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', Integer(4), Integer(1)], [[Integer(2),Integer(1)]])
>>> from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA
>>> bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[Integer(4),Integer(3)]]))
>>> bijection.cur_path.insert(Integer(0), [])
>>> bijection.cur_dims.insert(Integer(0), [Integer(0), Integer(1)])
>>> bijection.cur_path[Integer(0)].insert(Integer(0), [Integer(3)])
>>> bijection.next_state(Integer(3))

class sage.combinat.rigged_configurations.bij_type_A.RCToKRTBijectionTypeA(RC_element)

Bases: 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

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

Python

>>> from sage.all import *
>>> RC = RiggedConfigurations(['A', Integer(4), Integer(1)], [[Integer(2), Integer(1)]])
>>> from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA
>>> bijection = RCToKRTBijectionTypeA(RC(partition_list=[[Integer(1)],[Integer(1)],[Integer(1)],[Integer(1)]]))
>>> bijection.next_state(Integer(1))
5