Bijection classes for type \(E_{6,7}^{(1)}\)

Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(E_{6,7}^{(1)}\).

AUTHORS:

  • Travis Scrimshaw (2011-04-15): Initial version

class sage.combinat.rigged_configurations.bij_type_E67.KRTToRCBijectionTypeE67(tp_krt)[source]

Bases: KRTToRCBijectionAbstract

Specific implementation of the bijection from KR tableaux to rigged configurations for type \(E_{6,7}^{(1)}\).

next_state(val)[source]

Build the next state for type \(E_{6,7}^{(1)}\).

class sage.combinat.rigged_configurations.bij_type_E67.RCToKRTBijectionTypeE67(RC_element)[source]

Bases: RCToKRTBijectionAbstract

Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(E_{6,7}^{(1)}\).

next_state(r)[source]

Build the next state for type \(E_{6,7}^{(1)}\).

sage.combinat.rigged_configurations.bij_type_E67.endpoint6(r)[source]

Return the endpoint for \(B^{r,1}\) in type \(E_6^{(1)}\).

EXAMPLES:

sage: from sage.combinat.rigged_configurations.bij_type_E67 import endpoint6
sage: endpoint6(1)
(1,)
sage: endpoint6(2)
(-3, 2)
sage: endpoint6(3)
(-1, 3)
sage: endpoint6(4)
(-3, 4)
sage: endpoint6(5)
(-2, 5)
sage: endpoint6(6)
(-1, 6)
>>> from sage.all import *
>>> from sage.combinat.rigged_configurations.bij_type_E67 import endpoint6
>>> endpoint6(Integer(1))
(1,)
>>> endpoint6(Integer(2))
(-3, 2)
>>> endpoint6(Integer(3))
(-1, 3)
>>> endpoint6(Integer(4))
(-3, 4)
>>> endpoint6(Integer(5))
(-2, 5)
>>> endpoint6(Integer(6))
(-1, 6)
sage.combinat.rigged_configurations.bij_type_E67.endpoint7(r)[source]

Return the endpoint for \(B^{r,1}\) in type \(E_7^{(1)}\).

EXAMPLES:

sage: from sage.combinat.rigged_configurations.bij_type_E67 import endpoint7
sage: endpoint7(1)
(-7, 1)
sage: endpoint7(2)
(-1, 2)
sage: endpoint7(3)
(-2, 3)
sage: endpoint7(4)
(-5, 4)
sage: endpoint7(5)
(-6, 5)
sage: endpoint7(6)
(-7, 6)
sage: endpoint7(7)
(7,)
>>> from sage.all import *
>>> from sage.combinat.rigged_configurations.bij_type_E67 import endpoint7
>>> endpoint7(Integer(1))
(-7, 1)
>>> endpoint7(Integer(2))
(-1, 2)
>>> endpoint7(Integer(3))
(-2, 3)
>>> endpoint7(Integer(4))
(-5, 4)
>>> endpoint7(Integer(5))
(-6, 5)
>>> endpoint7(Integer(6))
(-7, 6)
>>> endpoint7(Integer(7))
(7,)