ebadekvaatsed

Ebadekvaatsed is a term used in Estonian-language discussions of mathematics and related disciplines to describe objects that are not equivalent under a specified relation or symmetry. In practice, the notion is used to distinguish distinct configurations, representations, or structures when symmetry or an equivalence relation identifies some objects as the same. The concept appears in combinatorics, geometry, and chemistry, as well as in abstract algebra, where counting non-equivalent cases is common.

Definition and framework: Suppose a set X carries an action of a group G, so two elements x and y are considered equivalent if there exists g in G with g.x = y. Then x and y are ebadekvaatsed if they lie in different orbits of G; equivalently, they are not related by the chosen symmetry. The particular choice of G, i.e., which symmetries are considered, determines which objects are ebadekvaatsed.

Counting and methods: The number of ebadekvaatsed configurations equals the number of orbits of X under G. Burnside's lemma and related orbit-counting techniques are standard tools for such calculations. Examples often appear in coloring problems, tilings, and stereoisomerism, where one counts arrangements modulo symmetry. The term emphasizes that the classification depends on the selected notion of equivalence rather than on intrinsic differences alone.

Usage and notes: The term is primarily used in Estonian-language texts and education; in English-language contexts the concept is usually described with phrases such as non-equivalent or distinct up to symmetry. In practice, researchers specify the symmetry group or relation first, then identify which objects remain distinct under that specification.