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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. 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! This method has been developed for the purpose of enumerating triangulations up to symmetry. See Joswig, Jordan and Kastner, Electron. J. Combin. 25.3, Paper 3.6, 27. It is used in mptopcom, https://polymake.org/mptopcom .
 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: 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
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. For more details see
SWITCH_TABLE
.

lex_minimal
Similar to
lex_maximal
; for more details seeSWITCH_TABLE
.