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

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# 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)

  Bases: `KRTToRCBijectionAbstract`

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

  next_state(val)

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

class sage.combinat.rigged_configurations.bij_type_E67.RCToKRTBijectionTypeE67(RC_element)

  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)

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

sage.combinat.rigged_configurations.bij_type_E67.endpoint6(r)

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

  EXAMPLES:

  Sage

      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)

  Python

      >>> 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)

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

  EXAMPLES:

  Sage

      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,)

  Python

      >>> 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,)