This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== BigObject PermutationAction ====== //from application [[..:group|group]]//\\ \\ derived objects for permutation representations ? derived from: : ''[[..:group:Action |Action]]'' ===== Properties ===== ==== Orbits ==== Dealing with orbits under permutation groups. ---- {{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> ---- ==== 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]]%%>>%%'' ---- {{anchor:transversals:}} ? **''TRANSVERSALS''** :: Transversals along the stabilizer chain. ? Type: :''[[..:common#Array |Array]]<[[..:common#Array |Array]]<[[..:common#Int |Int]]%%>>%%'' ---- {{anchor:transversal_sizes:}} ? **''TRANSVERSAL_SIZES''** :: The number of group elements per transversal. ? Type: :''[[..:common#Array |Array]]<[[..:common#Int |Int]]>'' ---- ===== Methods ===== ==== Orbits ==== Dealing with orbits under permutation groups. ---- {{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 ---- {{anchor:lex_minimal:}} ? **''lex_minimal''** :: Similar to ''[[..:group:PermutationAction#lex_maximal |lex_maximal]]''. ---- documentation/release/4.2/group/permutationaction.txt Last modified: 2020/09/10 17:50by 127.0.0.1