In this chapter we mention a couple functions that are fairly basic but useful tools to work with.
‣ PermComplement( perm ) | ( function ) |
Returns: The permutation that is the complement of perm.
The complement of a permutation \(\tau=\tau_{1}\ldots\tau_{n}\) is the permutation
\[\tau^{C}=(n+1)-\tau_{1}\ \ (n+1)-\tau_{2}\ldots (n+1)-\tau_{n}\]
.
gap> PermComplement([3,2,8,6,7,1,5,4]); [ 6, 7, 1, 3, 2, 8, 4, 5 ] gap>
‣ IsRankEncoding( perm ) | ( function ) |
Returns: true if perm is a valid rank encoding of a permutation.
IsRankEncoding checkes whether the input list perm is a valid rank encoding by checking whether it is accepted by the bounded class automaton, with the highest rank being set by the highest element in perm.
gap> IsRankEncoding([3,2,6,4,4,1,2,1]); true gap> IsRankEncoding([3,2,6,4,5,1,2,1]); false gap>
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