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The image of a point i under a partial permutation f is expressed as i^f in GAP. In this way, partial permutations are the elements of inverse partial permutation semigroups.Ī partial permutations in GAP acts on a finite set of positive integers on the right. The largest point on which a partial permutation can be defined, and the largest value that the image of such a point can have, are defined by certain architecture dependent limits.Įvery inverse semigroup is isomorphic to an inverse semigroup of partial permutations and, as such, partial permutations are to inverse semigroup theory what permutations are to group theory and transformations are to semigroup theory. This chapter describes the functions in GAP for partial permutations.Ī partial permutation in GAP is simply an injective function from any finite set of positive integers to any other finite set of positive integers.

54.7-6 IsomorphismPartialPermSemigroup 54 Partial permutations