täispermutatsiooniga

The Estonian term täispermutatsiooniga refers to arrangements in which all elements of a set are permuted without repetition. In combinatorial mathematics a full or complete permutation of a set with n distinguishable elements is a bijection from the set onto itself; each element occupies exactly one position in the resulting sequence. The number of such permutations is n factorial (n!).

A täispermutatsiooniga can be represented by a permutation matrix, an n×n matrix containing exactly one entry of 1 in each row and column, with all other entries 0. The product of a permutation matrix and a vector of coordinates yields the coordinates rearranged according to the permutation. In cycle notation a full permutation may be decomposed into disjoint cycles, each cycle being a sequence of elements that map to each other in a cyclic fashion.

Applications of the concept include the analysis of shuffling algorithms, cryptographic key schedules, and the study of symmetric groups in group theory. It also underlies permutations used in combinatorial designs and in modeling of random processes where all outcomes are equally likely. Because each element is used exactly once, full permutations avoid repetition, making them suitable for tasks requiring exhaustive rearrangements such as assigning unique tasks or distributing resources.

The term täispermutatsiooniga thus denotes any operation or context where a perfect, one-to-one mapping of all elements of a finite set is intended, emphasizing the completeness and exclusivity of the rearrangement.