====== BigObject PermutationAction ======
//from application [[..:group|group]]//\\
\\
 derived objects for permutation representations

  ? derived from:
  : ''[[..:group:Action |Action]]''
===== Properties =====

==== Orbits ====
 Dealing with orbits under permutation groups.
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{{anchor:switch_table:}}
  ?  **''SWITCH_TABLE''**
  :: A switch table is a tool for finding lex-maximal or -minimal in orbits under the action of a permutation group. Its main ingredient is an upper-left triangular matrix with group elements as entries. See https://arxiv.org/abs/1709.04746 The output contains the support at every level, i.e. a number and a Set<Int>, the number is the size of the support and and the Set<Int> are the indices of those entries that can be permuted to the index of the current level while keeping previous level indices fixed. I.e. entry [i,j] will keep the first i entries of a vector fixed, while moving the j-th entry to position i. Note that we start counting at 0!
    ? Type:
    :''[[..:group#SwitchTable |SwitchTable]]''
    ? Example:
    :: <code perl> > $P = new PermutationAction(GENERATORS=>[[1,2,0,4,5,3],[2,1,0,5,4,3]]);
 > print $P->SWITCH_TABLE;
   Supports: (size, content)
 Level 0: 2 {1 2}
 Level 1: 1 {2}
   Entries:
 [0,1]: 1 0 2 4 3 5
 [0,2]: 1 2 0 4 5 3
 [1,2]: 0 2 1 3 5 4
</code>


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==== no category ====
{{anchor:base:}}
  ?  **''BASE''**
  :: A base for ''[[..:group:PermutationAction#STRONG_GENERATORS |STRONG_GENERATORS]]''.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Int |Int]]>''


----
{{anchor:n_strong_generators:}}
  ?  **''N_STRONG_GENERATORS''**
  :: The number of ''[[..:group:PermutationAction#STRONG_GENERATORS |STRONG_GENERATORS]]''.
    ? Type:
    :''[[..:common#Int |Int]]''


----
{{anchor:strong_generators:}}
  ?  **''STRONG_GENERATORS''**
  :: Strong generating set with respect to ''[[..:group:PermutationAction#BASE |BASE]]''.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Array |Array]]<[[..:common#Int |Int]]%%>>%%''


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{{anchor:transversals:}}
  ?  **''TRANSVERSALS''**
  :: Transversals along the stabilizer chain. 
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Array |Array]]<[[..:common#Int |Int]]%%>>%%''


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{{anchor:transversal_sizes:}}
  ?  **''TRANSVERSAL_SIZES''**
  :: The number of group elements per transversal.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Int |Int]]>''


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===== Methods =====

==== Orbits ====
 Dealing with orbits under permutation groups.
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{{anchor:lex_maximal:}}
  ?  **''lex_maximal''**
  :: Assume the group acts on a vector by permuting its entries. Then this method gives the lex-maximal vector from the orbit of the input vector under the group action. See https://arxiv.org/abs/1709.04746


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{{anchor:lex_minimal:}}
  ?  **''lex_minimal''**
  :: Similar to ''[[..:group:PermutationAction#lex_maximal |lex_maximal]]''.


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