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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
BigObject PermutationAction
Properties
Orbits
Dealing with orbits under permutation groups.

SWITCH_TABLE
A switch table is a tool for finding lexmaximal or minimal in orbits under the action of a permutation group. Its main ingredient is an upperleft 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 jth entry to position i. Note that we start counting at 0!
 Type:
 Example:
> $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: 3 {0 1 2} Level 1: 2 {1 2} Entries: [0,0]: 0 1 2 3 4 5 [0,1]: 1 0 2 4 3 5 [0,2]: 1 2 0 4 5 3 [1,1]: 0 1 2 3 4 5 [1,2]: 0 2 1 3 5 4
no category

BASE
A base for
STRONG_GENERATORS
. Type:

N_STRONG_GENERATORS
The number of
STRONG_GENERATORS
. Type:

STRONG_GENERATORS
Strong generating set with respect to
BASE
. Type:

TRANSVERSALS
Transversals along the stabilizer chain.
 Type:

TRANSVERSAL_SIZES
The number of group elements per transversal.
 Type:
Methods
Orbits
Dealing with orbits under permutation groups.

lex_maximal
Assume the group acts on a vector by permuting its entries. Then this method gives the lexmaximal vector from the orbit of the input vector under the group action. See https://arxiv.org/abs/1709.04746

lex_minimal
Similar to
lex_maximal
.