Partial permutation

In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of S. That is, it is defined by two subsets U and V of equal size, and a one-to-one mapping from U to V. Equivalently, it is a partial function on S that can be extended to a permutation.^[1]^[2]

^ Straubing, Howard (1983), "A combinatorial proof of the Cayley-Hamilton theorem", Discrete Mathematics, 43 (2–3): 273–279, doi:10.1016/0012-365X(83)90164-4, MR 0685635.
^ Ku, C. Y.; Leader, I. (2006), "An Erdős-Ko-Rado theorem for partial permutations", Discrete Mathematics, 306 (1): 74–86, doi:10.1016/j.disc.2005.11.007, MR 2202076.