information:classification, structural:expansion
Restricted partial permutations

Some authors restrict partial permutations so that either the domain or the range of the bijection is forced to consist of the first k items in the set of n items being permuted, for some k. In the former case, a partial permutation of length k from an n -set is just a sequence of k terms from the n -set without repetition. (In elementary combinatorics, these objects are sometimes confusingly called " k -permutations " of the n -set.)