erisuuret

Erisuuret is a Finnish mathematical term used to describe a collection of numbers in which no two elements have the same value. In practice, a sequence or multiset is called erisuuri if all its elements are pairwise distinct. For example, the sequence (3, 7, 15) is erisuuri, whereas (3, 3, 7) is not because 3 occurs twice. The term is used across combinatorics, number theory, and computer science to enforce a constraint of uniqueness.

Etymology: erisuuri is formed from eri- meaning "different" and suuri meaning "size" or "magnitude," reflecting the idea of distinct magnitudes.

Formal definition: Given a finite sequence (a1, a2, ..., an), it is erisuuri if ai ≠ aj for all i ≠ j. In set form, a finite set S is erisuuri when all elements are distinct, i.e., duplicates are not allowed.

Applications: In selection problems, restricting choices to erisuuret elements prevents repetition. In hash tables and coding, ensuring distinct keys or codewords; in geometry and design, enforcing uniqueness of side lengths or dimensions; in statistical data analysis, to identify and handle duplicates.

Variants: Some texts distinguish "strictly erisuuri" as explicitly pairwise distinct, while others use erisuuri more loosely to mean any set without repetition.

See also: distinct elements, injective maps, permutation, combination without repetition, uniqueness constraint.